Clifford Algebras as Twisted Group Algebras and the Arf Invariant
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DOI: 10.1007/s00006-018-0862-y
Abstract: Some connections between quadratic forms over the field of two elements, Clifford algebras of quadratic forms over the real numbers, real graded division algebras, and twisted group algebras will be highlighted. This allows to revisit… read more here.
Keywords: algebras twisted; arf invariant; group algebras; twisted group ... See more keywords
Homomorphisms and Rigid Isomorphisms of Twisted Group Doubles
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DOI: 10.1007/s10468-019-09871-x
Abstract: We prove several results concerning quasi-bialgebra morphisms D ω ( G ) → D η ( H ) ${\mathcal {D}^{\omega }(G)\to \mathcal {D}^{\eta }(H)}$ of twisted group doubles. We take a particular focus on the… read more here.
Keywords: group doubles; homomorphisms rigid; group; twisted group ... See more keywords
The twisted group ring isomorphism problem over fields
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DOI: 10.1007/s11856-020-2017-9
Abstract: Similarly to how the classical group ring isomorphism problem asks, for a commutative ring R , which information about a finite group G is encoded in the group ring RG , the twisted group ring… read more here.
Keywords: isomorphism problem; ring isomorphism; group; twisted group ... See more keywords