Crossed Products as Twisted Category Algebras

Danz, Susanne; Erdmann, Karin

doi:10.1007/s10468-014-9493-8

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2016

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Cited by 3 publications

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“…Let G be a group. Denote by •(g) the order of g ∈ G. Since C is algebraically closed we may always assume that for any f ∈ Z 2 (G, C * ), (7) u…”

Section: Preliminariesmentioning

confidence: 99%

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Simple Twisted Group Algebras of Dimensionp⁴and their Semi-Centers

Schnabel

2016

Communications in Algebra

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For simple twisted group algebra over a group G, if G is Hall subgroup of G then the semi-center is simple. Simple twisted groups algebras correspond to groups of central type. We classify all groups of central type of order p 4 where p is prime and use this to show that for odd primes p there exists a unique group G of order p 4 such that there exists simple twisted group algebra over G with a commutative semi-center. Moreover, if 1 < |G| < 64, then the semi-center of simple twisted group algebras over G is non-commutative and this bounds are strict.

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“…Let G be a group. Denote by •(g) the order of g ∈ G. Since C is algebraically closed we may always assume that for any f ∈ Z 2 (G, C * ), (7) u…”

Section: Preliminariesmentioning

confidence: 99%

“…Evidently, the size of any group of central type is a square. It turns out that twisted group algebras and groups of central type play a major role in the understanding of other algebraic objects, as graded algebras (see [3], [10], [11]), semi-invariants of matrices (see [12]) and twisted category algebras (see [7], [15]).…”

Section: Introductionmentioning

confidence: 99%

Simple Twisted Group Algebras of Dimensionp⁴and their Semi-Centers

Schnabel

2016

Communications in Algebra

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8 Categories and Groupoids

Steinberg

2016

Representation Theory of Finite Monoids

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Hopf automorphisms and twisted extensions

2016

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Abstract. We give some applications of a Hopf algebra constructed from a group acting on another Hopf algebra A as Hopf automorphisms, namely Molnar's smash coproduct Hopf algebra. We find connections between the exponent and Frobenius-Schur indicators of a smash coproduct and the twisted exponents and twisted Frobenius-Schur indicators of the original Hopf algebra A. We study the category of modules of the smash coproduct.

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Crossed Products as Twisted Category Algebras

Cited by 3 publications

References 16 publications

Simple Twisted Group Algebras of Dimensionp⁴and their Semi-Centers

Simple Twisted Group Algebras of Dimensionp⁴and their Semi-Centers

8 Categories and Groupoids

Hopf automorphisms and twisted extensions

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Crossed Products as Twisted Category Algebras

Cited by 3 publications

References 16 publications

Simple Twisted Group Algebras of Dimensionp4and their Semi-Centers

Simple Twisted Group Algebras of Dimensionp4and their Semi-Centers

8 Categories and Groupoids

Hopf automorphisms and twisted extensions

Contact Info

Product

Resources

About

Simple Twisted Group Algebras of Dimensionp⁴and their Semi-Centers

Simple Twisted Group Algebras of Dimensionp⁴and their Semi-Centers