Sara Westreich

Bar Ilan University | BIU · Department of Management

Conjugacy classes for groups were generalized in previous works of the authors to semisimple Hopf algebras over algebraically closed fields of characteristic zero. An essential property of the set of conjugacy classes { C j } \{\mathfrak {C}_j\} is that they are irreducible representations of the quantum double D ( H ) D(H) of H . H. We show that m...

In healthcare institutions, reporting and handling of near-miss events—events that could have resulted in catastrophe but did not—are considered crucial to patient safety. Empirical studies have explored factors that influence near-miss reporting behavior in specific healthcare settings, yet they are limited in their capacity to provide general ins...

We analyze a dual-channel supply chain comprising two suppliers that offer vertically-differentiated agricultural products; specifically, one offers an organic version of an agricultural product and the other offers a conventionally-grown version of the same product. Each supplier distributes his product through two channels: directly to consumers...

Near-miss safety events—unplanned incidents that reveal the potential for future adverse events—have an important yet complex role in workplace safety: If reported and handled correctly, they can contribute to the improvement of safety procedures, yet if they are mishandled, the likelihood of subsequent adverse events might increase. This research...

We show that for any solvable group G and a Drinfel'd twist J, kGJ is solvable in the sense of the intrinsic definition of solvability given in [2]. More generally, if a Hopf algebra H has a normal solvable series so does HJ. Furthermore, while solvable groups are defined as having certain commutative quotients, quasitriangular normally solvable Ho...

Reporting of near-miss safety events is commonly assumed to enhance safety in organizations, as such reporting enables managers to identify and address accident risk factors. An organization's capacity to leverage near-miss events in this way is contingent on cooperation between employees, who must report near-miss events accurately, and managers,...

In recent years, scholars have argued that traditional learning no longer achieves its goals because learning time is used inefficiently. The present goal is to demonstrate a way to more effectively utilize learning time in order to maximize knowledge. The model suggests a production function of education that includes interdependency between lectu...

Idle time is an essential and valuable factor in the production of any service. While idle time is necessary and helpful for efficient and effective utilization of time, it also has a negative effect that managers try to minimize. This paper illustrates either analytically or numerically the different effects of idle time on total net revenue. It f...

We consider pricing decisions of agri-food retailers offering organic versions and non-organic conventional versions of a single agricultural product, where the two product versions differ from each other in terms of their shelf lives and their utility to customers. The latter is captured in a random “valuation” variable distributed among customers...

We use integrals of left coideal subalgebras to develop Harmonic analysis for semisimple Hopf algebras. We show how $N^*,$ the space of functional on $N,$ is embedded in $H^*.$ We define a bilinear form on $N^*$ and show that irreducible $N$-characters are orthogonal with respect to that form. We then give an explicit formula for induced characters...

In this paper we investigate nilpotenct and probabilistically nilpotent Hopf algebras. We define nilpotency via a descending chain of commutators and give a criterion for nilpotency via a family of central invertible elements. These elements can be obtained from a {\it commutator matrix} $A$ which depends only on the Grothendieck ring of $H.$ When...

Let $H$ be a semisimple Hopf algebras over an algebraically closed field $k$ of characteristic $0.$ We define Hopf algebraic analogues of commutators and their generalizations and show how they are related to $H',$ the Hopf algebraic analogue of the commutator subgroup. We introduce a family of central elements of $H',$ which on one hand generate $...

We extend the pioneering work of Aumann–Serrano by presenting an index of riskiness for gambles with either positive or negative expectations. It can be of use for a variety of abstract behaviors, when adapting the framework of either Expected-Utility Theory or Prospect Theory.

We continue studying normal left coideal subalgebras of a Hopf algebra H, realizing them as invariants of H under the left hit action of Hopf subalgebras of H*. We apply this realization to test an equivalence relation on irreducible characters for two important examples. The commutator sublagebra of H, which is the analogue of the commutator subgr...

We continue studying properties of semisimple Hopf algebras $H$ over algebraically closed fields of characteristic 0 resulting from their generalized character tables. We show that just as normal subgroups of a finite group can be recovered from its character table so does the generalized character table of $H$ reflect the normal left coideal subal...

We continue studying properties of semisimple Hopf algebras $H$ over algebraically closed fields of characteristic 0 resulting from their generalized character tables. We show that the generalized character table of $H$ reflect normal left coideal subalgebras of $H.$ These are the Hopf analogues of normal subgroups in the sense that they arise from...

We extend the notion of conjugacy classes and class sums from finite groups to semisimple Hopf algebras and show that the conjugacy classes are obtained from the factorization of H as irreducible left D(H)-modules. For quasitriangular semisimple Hopf algebras H, we prove that the product of two class sums is an integral combination of the class sum...

We offer a comprehensive discussion on Verlinde-type formulas for Hopf algebras H over an algebraically closed field of characteristic 0. Some of the results are new and some are known, but are reproved from the point of view of symmetric algebras and the associated Higman (trace) map. We give an explicit form for the central Casimir element of C(H...

There have been many attempts, theoretical and empirical, to explain the persistence of a favorite-longshot bias in various horse betting markets. Most recently, Snowberg and Wolfers (2010) have shown that the data for the US markets support a misperceptions of probability approach in line with prospect theory over a neoclassical approach of the Qu...

Let k be an algebraically closed field of characteristic 0. In this paper we continue our study of structure constants for semisimple Hopf algebras H whose character algebra is commutative, and for non-semisimple factorizable ribbon Hopf algebras. This is done from the point of view of symmetric algebras, such as group algebras. In particular we co...

We present an empirical framework for determining whether or not customers at the roulette wheel are risk averse or risk loving. Thus, we present a summary of the Aumann-Serrano (2007) risk index as generalized to allow for the presence of risk lovers by Schnytzer and Westreich (2010). We show that, for any gamble, whereas riskiness increases for g...

In general, models in finance assume that investors are risk averse. An example of such a recent model is the pioneering work of Aumann and Serrano, which presents an economic index of riskiness of gambles which is independent of wealth and holds (as might be understood from the adjective “economic”) for exclusively risk averse investors. In their...

Given any bialgebra A and a braiding product 〈|〉 on A, a bialgebra U〈|〉 was constructed in [R. Larson, J. Towber, Two dual classes of bialgebras related to the concepts of “quantum group” and “quantum Lie algebra”, Comm. Algebra 19 (1991) 3295–3345], contained in the finite dual of A. This construction generalizes a (not very well known) constructi...

We extend the pioneering work of Aumann and Serrano by presenting an index of inherent riskiness of a gamble having the desirable properties of their index, while being applicable to gambles with either positive or negative expectations. As such, our index provides a measure of riskiness which is of use for both risk lovers and risk aversive gamble...

We study certain aspects of finite-dimensional non-semisimple symmetric Hopf algebras H and their duals H∗. We focus on the set I(H) of characters of projective H-modules which is an ideal of the algebra of cocommutative elements of H∗. This ideal corresponds via a symmetrizing form to the projective center (Higman ideal) of H which turns out to be...

We study pointed Hopf algebras of the form U(R Q ), (Faddeev et al., Quantization of Lie groups and Lie algebras. Algebraic Analysis, vol. I, Academic, Boston, MA, pp. 129–139, 1988; Faddeev et al., Quantum groups. Braid group, knot theory and statistical mechanics. Adv. Ser. Math. Phys., vol. 9, World Science, Teaneck, NJ, pp. 97–110, 1989; Larso...

Usual Fourier transforms for groups are related to integrals. All finite-dimensional and some infinite-dimensional Hopf algebras give rise to integrals, which define in turn Fourier transforms for these Hopf algebras. We first study these Fourier transforms Ψ, and the convolution product induced by them. “Quantum Fourier transforms” F were defined...

The cocommutative elements of the dual of the double D∗(H), which are the trace-like functionals on D(H), of the Taft (Hopf) algebra H over a field k are studied in detail. The subalgebra of cocommutative elements of D∗(H) is isomorphic to the center of D(H). Trace-like functionals on D(H) determine regular isotopy invariants of oriented knots and...

In this paper we study certain interrelations between subsets of Hopf algebras H and their duals which stem from various morphisms T defined on H. We define and study T-cocommutative elements. Cocommutative elements, generators of H as an H∗-module and invariants under various actions and coactions are all examples. An important role is played by N...

Two "quantum enveloping algebras", here denoted by $U(R)$ and $U^{\sim}(R)$, are associated in [FRTa] and [FRTb] to any Yang-Baxter operator R. The latter is only a bialgebra, in general; the former is a Hopf algebra. In this paper, we study the pointed Hopf algebras $U(R_Q)$, where $R_Q$ is the Yang-Baxter operator associated with the multi-parame...

In this paper we determine when Lusztig’s U q ( s l n ) ′ U_q(sl_n)’ has all the desired properties necessary to define invariants of knots, links and 3-manifolds. Specifically, we determine when it is ribbon, unimodular and factorizable. We also compute the integrals and distinguished elements involved.

In this paper we determine when Lusztig's Uq(sln)′ has all the desired properties necessary to define invariants of knots, links and 3-manifolds. Specifically, we determine when it is ribbon, unimodular and factorizable. We also compute the integrals and distinguished elements involved.

A Yetter—Drinfeld category over a Hopf algebra H with a bijective antipode, is equipped with a ‘braiding’ which may be symmetric for some of its subcategories (e.g. when H is a triangular Hopf algebra). We prove that under an additional condition (which we term the u-condition) such symmetric subcategories completely resemble the category of vector...

We consider the problem of the classification of semisimple Hopf algebras A of dimension pq where p < q are two prime numbers. First we prove that the order of the group of grouplike elements of A is not q, and that if it is p, then q = 1 (mod p). We use it to prove that if A and its dual Hopf algebra A* are of Frobenius type, then A is either a gr...

The quantum group Uq(sln) introduced by Drinfel'd [2] and Jimbo [5] is a Hopf algebra which is naturally paired with Oq(SLn), the coordinate ring of quantum SLn. When q is not a root of unity, the finite dimensional representation theory of Uq(sln) is essentially the same as that of U(sln). Furthermore, it is known that Uq(sln) is essentially a qua...

The aim of this paper is to generalize Noether’s theorem for finite groups acting on commutative algebras, to finite-dimensional triangular Hopf algebras acting on quantum commutative algebras. In the process we construct a non-commutative determinant function which yields an analogue of the Cayley-Hamilton theorem for certain endomorphisms.

In this paper we prove some properties of the set of group-like elements of A, G(A), for a pointed minimal quasitriangular Hopf algebra A over a eld k of characteristic 0, and for a pointed quasitriangular Hopf algebra which is indecomposable as a coalgebra. We rst show that over a eld of characteristic 0, for any pointed minimal quasitriangular Ho...

LetH be a Hopf algebra andM a representation or a corepresentation ofH. In this paper we study semiinvariants ofM. This notion generalizes the known concept of weight spaces in the context of representations of Lie algebras. Our best results are attained for pointed Hopf algebras, and semiinvariants which are related to the coradical filtration ofH...

Let (H, R) be a triangular Hopf algebra and let V be a finite-dimensional representation of H. Following Manin we imitate the standard algebraic constructions in order to define the relativized notions of R-universal enveloping algebras of R-Lie algebras and the R-Lie algebra glR(V). Using Majid's "bosonization" theorem and the above we prove an R-...

Let (H, R) be a quasitriangular Hopf algebra acting on an algebra A. We study a concept of A being quantum commutative with respect to (H, R). Superalgebras which are graded commutative (called sometimes commutative superalgebras) are shown to be examples of such an action. There is an analogous notion of quantum commutativity for comodule algebra....

Let H be a Hopf algebra over a field k, and A an H-module algebra, with subalgebra of H-invariants denoted by A(H). When (H, R) is quasitriangular and A is quantum commutative with respect to (H, R), (e.g. quantum planes, graded commutative superalgebras), then A(H) subset-of center of A = Z(A). In this paper we are mainly concerned with actions of...