7 papers
Gradings by cyclic groups on classical simple Lie algebras in prime characteristics
Mikhail Kochetov, Vishal Yadav
We classify, up to isomorphism, gradings by finite cyclic groups on classical simple Lie algebras over an algebraically closed field of arbitrary characteristic. Usi…
Generic graded contractions of Lie algebras
Mikhail V. Kochetov, Serhii D. Koval
We study generic graded contractions of Lie algebras from the perspectives of group cohomology, affine algebraic geometry and monoidal categories. We show that generic graded contr…
Special pure gradings on simple Lie algebras of types , ,
Cristina Draper, Alberto Elduque, Mikhail Kochetov
A group grading on a semisimple Lie algebra over an algebraically closed field of characteristic zero is special if its identity component is zero; it is pure if at least one of it…
Direct limits of graded matrix algebras
Mikhail Kochetov, Felipe Yasumura
The direct limit of finite-dimensional semisimple associative algebras arises as a purely algebraic counterpart to important -algebras. In this paper, we classify direct li…
Group gradings on classical Lie superalgebras
Caio De Naday Hornhardt, Mikhail Kochetov
We classify, up to isomorphism, the group gradings on the non-exceptional classical simple Lie superalgebras, except for type A(1,1), over an algebraically closed field of characte…
Almost fine gradings on algebras and classification of gradings up to isomorphism
Alberto Elduque, Mikhail Kochetov
We consider the problem of classifying gradings by groups on a finite-dimensional algebra (with any number of multilinear operations) over an algebraically closed field. We int…