7 papers
Quantum regularity of finite dimensional semisimple algebras
Yuri Bahturin, Lucio Centrone, Kauê Pereira
In this paper, we establish a necessary and sufficient criterion for a finite-dimensional semisimple algebra over an algebraically closed field of characteristic to admit a reg…
Finite basis property for finite graded algebras
Yuri Bahturin, Daniela Martinez Correa, Diogo Diniz
Let be a finite group and let $\F$ be a finite field. We prove that any finite-dimensional -graded associative algebra over $\F$ has a finite basis for its -graded po…
On Regular Quantum Commutative Algebras
Yuri Bahturin, Lucio Centrone, Kauê Pereira
Let be an algebraically closed field of characteristic different from . We provide a positive solution to the Bahturin--Regev conjecture in the general finite-dimensional (n…
Locally finite varieties of nonassociative algebras
Yuri Bahturin, Alexander Olshanskii
We study locally finite varieties (=primitive classes) of linear algebras over finite fields. We do not assume that our algebras are associative or Lie. We are interested in the ba…
Polynomial identities of finite prime Universal algebras
Yuri Bahturin, Daniela Martinez Correa, Diogo Diniz +1
We prove that two finite prime -algebras defined over the same unital commutative ring and satisfying the same set of polynomial identities are isomorphic.
Superpolynomial identities of finite-dimensional simple algebras
Yuri Bahturin, Felipe Yukihide Yasumura
We investigate the Grassmann envelope (of finite rank) of a finite-dimensional -graded algebra. As a result, we describe the polynomial identities of $G_1(\mathcal{A}…