Related papers: Is supernilpotence super nilpotence?

This expository article gives a thorough and well-motivated account of the proof of the nilpotence theorem by Devinatz-Hopkins-Smith.

Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.

We study group-graded Lie algebras L with finite support X. We show that L is nilpotent of |X|-bounded class if X is arithmetically-free. Conversely: we show that Y supports the grading of a non-nilpotent Lie algebra if Y is not…

The paper is devoted studying solvable Leibniz algebras with a nilradical possessing the codimension equals the number of its generators. We describe this class in non-split nilradical case. Then the case of split nilradical is worked out.…

We give a classification of the principal and distinguished nilpotent pairs in all classical Lie algebras. As a classification of the principal pairs in the exceptional simple Lie algebras was obtained earlier (see Appendix to Ginzburg's…

Let $(N,L)$ be a pair of finite dimensional nilpotent Lie algebras and $N$ admits a complement $K$ in $L$ such that $\dim N=n$ and $\dim K=m$. Let $s(N,L)=\frac{1}{2}(n-1)(n-2)+1+(n-1)m-\dim \M(N,L)$, where $\M(N,L)$ denotes the multiplier…

This paper is devoted to give the complete algebraic and geometric classification of $4$-dimensional nilpotent Novikov algebras over $\mathbb C.$

We determine the maximal dimension of totally geodesic subalgebras of N-graded filiform Lie algebras, and we show that these bounds are attained.

We give a classification of 5- and 6-dimensional complex one-generated nilpotent Novikov algebras

We construct a nil algebra over a countable field which has finite but non-zero Gelfand-Kirillov dimension.

Isoclinism of Lie superalgebras has been defined and studied currently. In this article it is shown that for finite dimensional Lie superalgebras of same dimension, the notation of isoclinism and isomorphism are equivalent. Furthermore we…

We give an algebraic classification of complex $5$-dimensional one-generated nilpotent terminal algebras.

The present article is a part of the study of solvable Leibniz algebras with a given nilradical. In this paper solvable Leibniz algebras, whose nilradicals is naturally graded quasi-filiform algebra and the complemented space to the…

Finite type nilpotent spaces are weakly equivalent if and only if their singular cochains are quasi-isomorphic as E-infinity algebras. The cochain functor from the homotopy category of finite type nilpotent spaces to the homotopy category…

We complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is…

We give a full classification of 6-dimensional nilpotent Lie algebras over an arbitrary field, including fields that are not algebraically closed and fields of characteristic~2. To achieve the classification we use the action of the…

I give a proof of Zel'manov's theorem that if $L$ is an $n$-Engel Lie algebra over a field $F$ of characteristic zero then $L$ is (globally) nilpotent. This is a very important result which extends Kostrikin's theorem that $L$ is locally…

In this paper we classify the isomorphism classes of four dimensional nilpotent associative algebras over a field F, studying regular subgroups of the affine group AGL_4(F). In particular we provide explicit representatives for such classes…

Suppose that a Lie type algebra L over a field K admits a Frobenius group of automorphisms FH with cyclic kernel F of order n and complement H such that the fixed-point subalgebra of F is trivial and the fixed-point subalgebra of H is…

We provide explicit formulas for the number of ad-nilpotent ideals of a Borel subalgebra of a complex simple Lie algebra having fixed class of nilpotence.