scholarly journals Symmetric algebras, skew category algebras and inverse semigroups

2012 ◽  
Vol 369 ◽  
pp. 226-234
Author(s):  
Constantin-Cosmin Todea
Keyword(s):  
Inverse Semigroups ◽  
Symmetric Algebras ◽  
Category Algebras

scholarly journals On inverse categories and transfer in cohomology

2012 ◽  
Vol 56 (1) ◽  
pp. 187-210 ◽  
Author(s):  
Markus Linckelmann
Keyword(s):  
Hochschild Cohomology ◽  
Abelian Groups ◽  
Mackey Functor ◽  
Symmetric Algebras ◽  
Transfer Maps ◽  
Category Algebras

AbstractIt follows from methods of B. Steinberg, extended to inverse categories, that finite inverse category algebras are isomorphic to their associated groupoid algebras; in particular, they are symmetric algebras with canonical symmetrizing forms.We deduce the existence of transfer maps in cohomology and Hochschild cohomology from certain inverse subcategories. This is in part motivated by the observation that, for certain categories $\mathcal{C}$, being a Mackey functor on $\mathcal{C}$ is equivalent to being extendible to a suitable inverse category containing $\mathcal{C}$. We further show that extensions of inverse categories by abelian groups are again inverse categories.

scholarly journals Inverse semigroups with idempotent-fixing automorphisms

2014 ◽  
Vol 89 (2) ◽  
pp. 469-474 ◽  
Author(s):  
João Araújo ◽  
Michael Kinyon
Keyword(s):  
Inverse Semigroups

PBW deformations of quantum symmetric algebras and their group extensions

2016 ◽  
Vol 15 (03) ◽  
pp. 1650049 ◽  
Author(s):  
Piyush Shroff ◽  
Sarah Witherspoon
Keyword(s):  
Finite Group ◽  
Lie Algebra ◽  
Sufficient Conditions ◽  
Necessary And Sufficient Conditions ◽  
Group Extensions ◽  
Enveloping Algebra ◽  
Symmetric Algebras ◽  
Necessary And Sufficient ◽  
Special Case

We examine PBW deformations of finite group extensions of quantum symmetric algebras, in particular the quantum Drinfeld orbifold algebras defined by the first author. We give a homological interpretation, in terms of Gerstenhaber brackets, of the necessary and sufficient conditions on parameter functions to define a quantum Drinfeld orbifold algebra, thus clarifying the conditions. In case the acting group is trivial, we determine conditions under which such a PBW deformation is a generalized enveloping algebra of a color Lie algebra; our PBW deformations include these algebras as a special case.

scholarly journals Characters and centers of symmetric algebras

1970 ◽  
Vol 16 (1) ◽  
pp. 4-13 ◽  
Author(s):  
T.V Fossum
Keyword(s):  
Symmetric Algebras

On certain codes admitting inverse semigroups as syntactic monoids

1974 ◽  
Vol 8 (1) ◽  
pp. 312-331 ◽  
Author(s):  
Michael Keenan ◽  
Gerard Lallement
Keyword(s):  
Inverse Semigroups

On Cayley Graphs of Inverse Semigroups

2006 ◽  
Vol 72 (3) ◽  
pp. 411-418 ◽  
Author(s):  
A.V. Kelarev
Keyword(s):  
Cayley Graphs ◽  
Inverse Semigroups
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