Related papers: Gradings on the Kac superalgebra

We classify up to equivalence the gradings on Hurwitz superalgebras and on symmetric composition superalgebras, over any field. Also, classifications up to isomorphism are given in case the field is algebraically closed. By grading, here we…

The group gradings on the symmetric composition algebras over arbitrary fields are classified. Applications of this result to gradings on the exceptional simple Lie algebras are considered too.

We classify gradings by arbitrary abelian groups on the classical simple Lie superalgebras $P(n)$, $n \geq 2$, and on the simple associative superalgebras $M(m,n)$, $m, n \geq 1$, over an algebraically closed field: fine gradings up to…

The group of automorphisms of the Kac Jordan superalgebra is described, and used to classify the maximal subalgebras.

The fine abelian group gradings on the simple exceptional classical Lie superalgebras over algebraically closed fields of characteristic 0 are determined up to equivalence.

We give a geometric classification of 4-dimensional superalgebras over an algebraic closed field.

We classify gradings by arbitrary abelian groups on the classical simple Lie and Jordan superalgebras $Q(n)$, $n \geq 2$, over an algebraically closed field of characteristic different from $2$ (and not dividing $n+1$ in the Lie case): fine…

Here, in every simple finite-dimensional vectorial Lie superalgebra considered with the standard grading where every indeterminate is of degree 1, the maximal graded solvable subalgebras are classified over $\mathbb{C}$.

We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.

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 characteristic zero. To this end, we study graded-simple and…

We classify gradings on matrix algebras by a finite abelian group. A grading is called good if all elementary matrices are homogeneous. For cyclic groups, all gradings on a matrix algebra over an algebraically closed field are good. We can…

We classify, up to isomorphism and up to equivalence, division gradings (by abelian groups) on finite-dimensional simple real algebras. Gradings on finite-dimensional simple algebras are determined by division gradings, so our results give…

We describe the fine (group) gradings on the Heisenberg algebras, on the Heisenberg superalgebras and on the twisted Heisenberg algebras. We compute the Weyl groups of these gradings. Also the results obtained respect to Heisenberg…

We classify crossed product gradings for arbitrary groups and fields up to several equivalence relations in terms of group actions and their orbits.

This is a matricial description of all the fine group gradings on the exceptional Lie algebra $o(8,\mathbb C)$. There are fourteen.

We classify up to isomorphism the gradings by arbitrary groups on the exceptional classical simple Lie superalgebras $G(3)$, $F(4)$ and $D(2,1;\alpha)$ over an algebraically closed field of characteristic $0$. To achieve this, we apply the…

Some fine gradings on the exceptional Lie algebras $\mathfrak{e}_6$, $\mathfrak{e}_7$ and $\mathfrak{e}_8$ are described. This list tries to be exhaustive.

We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.

A contragredient Lie superalgebra is a superalgebra defined by a Cartan matrix. A contragredient Lie superalgebra has finite-growth if the dimensions of the graded components (in the natural grading) depend polynomially on the degree. In…

The Hecke category is bigraded. For completeness, we classify gradings on the Hecke category. We also classify object-preserving autoequivalences.