Klaus W. Roggenkamp’s research while affiliated with Klinikum Stuttgart and other places

... For n > 0 and any δ ∈ k the functors G h and F h act as in (9) and (10) (These manipulations are essentially the same as in the Brauer case, see e.g. [19,54,55]. In this proposition our new geometrical constraints do not affect the argument.) ...

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On geometrically defined extensions of the Temperley-Lieb category in the Brauer category

... The presentation rank pr(G) of a finite group G is an invariant whose definition comes from the study of relation modules (see [4] for more details). Let I G denote the augmentation ideal of ZG, and d(I G ) the minimal number of elements of I G needed to generate I G as a G-module, then d(G) = d(I G ) + pr(G) [21]. It is known that pr(G) = 0 for many groups G, including all soluble groups, all Frobenius groups and all 2-generated groups. ...

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Coprime invariable generation and minimal-exponent groups

... For a somewhat more involved kind of reduction, which, however, gets specializations inside number fields, see the Geyer method treated in Roggenkamp [26]. ...

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Isomorphisms of p-adic Group Rings

... It is known that all groups of order < 96 have distinct table of marks [45]. Therefore, fusion of surface operators labelled by 2-representations uniquely determines any gauge group G with |G| < 96. ...

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On reconstructing finite gauge group from fusion rules

... Various aspects of tiled orders have been extensively studied in the literature. These include homological aspects [14,15,10,11,17,19,20,26,28], representation theory [27,32,33,34,39], structure [12,23,37,36,38], K-theory [18,22] and others. In addition, tiled orders turned out to be useful to prove Krull-Remak-Schmidt-Azumaya type theorems in additive categories [3] and, more recently, a strong connection between cluster categories and Cohen-Macaulay representation theory of some tiled orders was established in [4]. ...

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The max-plus algebra of exponent matrices of tiled orders

... Does an isomorphism of group algebras F p G ∼ = F p H for some group H imply an isomorphism of groups G ∼ = H? Sometimes though, e.g. in [56,Conjecture 9.4] or [18,2,51,9], it appears in the more general form on which we focus here: MIP over all fields: Let G be a finite p-group and F a field of characteristic p. ...

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The Modular Isomorphism Problem over all fields

... In Example 5.12 we checked that I is arrow-direct. It is clear that I is special and bounded below and so the quotient Λ = RQ/I is a string algebra over R. We shall show that Λ is an example 21 considered by Roggenkamp [61]. Let Γ = H 2 (R) × H 2 (R) and Hence if λ ∈ Λ then for some r 1 , r 2 r a , r b , r c , r d , r ac , r ca , r bd , r db ∈ R we have λ = y + I, y = r 1 e 1 + r 2 e 2 + r a a + r b b + r c c + r d d + r ac ac + r ca ca + r bd bd + r db db. ...

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String algebras over local rings: admissibility and biseriality

... For example, if for each ∈ 1 the arrows and̄lie in different g-orbits, then the [[ 1∕ ]]-orders Γ are hereditary with basis ( ) , for ⩽ and 1∕ ( ) , for > . This is perfectly analogous to the lifts of Brauer tree algebras to -adic discrete valuation rings that occur in blocks (also called 'Green orders' [39]). ...

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Bijections of silting complexes and derived Picard groups

... Indeed for each finite group G there is an abelian extension E := A ⋊ G such that (ZC2), and so also (IP), has a positive answer, i.e. different group bases of ZE are conjugate within QG. This follows from the F * -theorem which has been discovered by K.W.Roggenkamp and L.L.Scott [53], [52,Theorem 19] and has now finally a published account [26, Theorem A and p.350], see also [28, p.180]. With respect to semilocal coefficient rings the F * -theorem (in its automorphism version) may be stated as follows. ...

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Algorithmic aspects of units in group rings

... Theorem 1.3, applied to U = V , shows that if U is an indecomposable nonprojective lattice for a symmetric O-algebra A such that K ⊗ O A is separable, then the socle of End A (U ) as a module over itself is simple, since it is dual to End A (U )/J(End A (U )) ∼ = k. This fact is well-known -see Roggenkamp [18] -and this is the key step in the existence proof of almost split sequences of A-modules. Applying Theorem 1.3 to Heller translates of V yields non degenerate pairings Theorem 1.2 is a special case of the following consequence of Theorem 1.3 which gives a characterisation of absolutely indecomposable modules with the stable exponent property for symmetric O-algebras. ...

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On Tate duality and a projective scalar property for symmetric algebras