scholarly journals Graded polynomial identities for matrices with the transpose involution

2016 ◽  
Vol 464 ◽  
pp. 175-197 ◽  
Author(s):  
Darrell Haile ◽  
Michael Natapov
Keyword(s):  
Polynomial Identities ◽  
Graded Polynomial Identities

On the factorability of the ideal of ⁎-graded polynomial identities of minimal varieties of PI ⁎-superalgebras

2022 ◽  
Vol 589 ◽  
pp. 273-286
Author(s):  
Onofrio Mario Di Vincenzo ◽  
Viviane Ribeiro Tomaz da Silva ◽  
Ernesto Spinelli
Keyword(s):  
Polynomial Identities ◽  
Graded Polynomial Identities ◽  
The Ideal

scholarly journals On H-simple not necessarily associative algebras

2019 ◽  
Vol 18 (09) ◽  
pp. 1950162
Author(s):  
A. S. Gordienko
Keyword(s):  
Associative Algebra ◽  
Hopf Algebras ◽  
Simple Algebra ◽  
Polynomial Identities ◽  
Associative Algebras ◽  
Graded Algebras ◽  
Finite Dimensional ◽  
Graded Polynomial Identities ◽  
Group Gradings ◽  
Polynomial Formula

An algebra [Formula: see text] with a generalized [Formula: see text]-action is a generalization of an [Formula: see text]-module algebra where [Formula: see text] is just an associative algebra with [Formula: see text] and a relaxed compatibility condition between the multiplication in [Formula: see text] and the [Formula: see text]-action on [Formula: see text] holds. At first glance, this notion may appear too general, however, it enables to work with algebras endowed with various kinds of additional structures (e.g. comodule algebras over Hopf algebras, graded algebras, algebras with an action of a semigroup by anti-endomorphisms). This approach proves to be especially fruitful in the theory of polynomial identities. We show that if [Formula: see text] is a finite dimensional (not necessarily associative) algebra over a field of characteristic [Formula: see text] and [Formula: see text] is simple with respect to a generalized [Formula: see text]-action, then there exists [Formula: see text] where [Formula: see text] is the sequence of codimensions of polynomial [Formula: see text]-identities of [Formula: see text]. In particular, if [Formula: see text] is a finite dimensional (not necessarily group graded) graded-simple algebra, then there exists [Formula: see text] where [Formula: see text] is the sequence of codimensions of graded polynomial identities of [Formula: see text]. In addition, we study the free-forgetful adjunctions corresponding to (not necessarily group) gradings and generalized [Formula: see text]-actions.

Minimal supervarieties with factorable ideal of graded polynomial identities

2016 ◽  
Vol 220 (4) ◽  
pp. 1316-1330 ◽  
Author(s):  
Onofrio Mario Di Vincenzo ◽  
Viviane Ribeiro Tomaz da Silva ◽  
Ernesto Spinelli
Keyword(s):  
Polynomial Identities ◽  
Graded Polynomial Identities
Sign in / Sign up

Export Citation Format

Share Document