Fereshte BahadorykhalilyInstitute for Advanced Studies in Basic Sciences | IASBS · Department of Mathematics
Fereshte Bahadorykhalily
Master of Science
Machine learning and data science
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Introduction
Publications
Publications (5)
A new generalization of Grassmannians to supergeometry, different from the well known supergrassmannian, is introduced. These are constructed by gluing a finite number of copies of a \nu\- domain, i.e. a superdomain with an odd involution, say \nu\, on their structure sheaf considered as a sheaf of C^\infty_{R^m}-modules.
http://www2.macaulay2.com/Macaulay2/doc/Macaulay2-1.18/share/doc/Macaulay2/SuperLinearAlgebra/html/index.html
The purpose of this short note is to consider multivariate Hasse-Schmidt derivations on exterior algebras and to show how they easily provide remarkable identities, holding in the algebra of square matrices, which generalize the classical theorem of Cayley–Hamilton.
The purpose of this short note is to consider multi-variate Hasse-Schmidt derivations on exterior algebras and to show that as they easily provide remarkable identities that hold in the algebra of square matrices, they also generalize the classical theorem of Cayley-Hamilton.
A new generalization of Grassmannians in supergeometry, called
ν−Grassmannians, are constructed by gluing ν−domains. By a ν−domain, we
mean a superdomain with an odd involution say ν on its structure sheaf, as
morphism of modules. Then we show that ν−Grassmannians are homogeneous
superspaces. In addition, in the last section, a supergroup associate...