Related papers: Supernilpotence prevents dualizability
A special case of a conjecture raised by Forrest and Runde (Math. Zeit., 2005) asserts that the Fourier algebra of every non-abelian connected Lie group fails to be weakly amenable; this was aleady known to hold in the non-abelian compact…
In this article we define the $c$-nilpotent multiplier of a finite dimensional Lie suepralgebra. We characterize the structure of $2$-nilpotent multiplier of finite dimensional nilpotent Lie superalgebras whose derived subalgebras have…
We study generalized complex structures and $T$-duality (in the sense of Bouwknegt, Evslin, Hannabuss and Mathai) on Lie algebras and construct the corresponding Cavalcanti and Gualtieri map. Such a construction is called "Infinitesimal…
In this paper we determine all finitely generated abelian groups which are varietal capable with respect to the variety of polynilpotent groups. This result is a vast generalization of the famous Baer's result about capability of finitely…
The paper is devoted to the investigation of finite dimensional commutative nilpotent (associative) algebras N over an arbitrary base field of characteristic zero. Due to the lack of a general structure theory for algebras of this type (as…
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 address two properties for Abelian topological groups: ``every closed subgroup is dually closed'' and ``every closed subgroup is dually embedded.'' We exhibit a pair of topological groups such that each has both of the properties and the…
Consider a pronilpotent DG (differential graded) Lie algebra over a field of characteristic 0. In the first part of the paper we introduce the reduced Deligne groupoid associated to this DG Lie algebra. We prove that a DG Lie…
In this paper we continue the investigations on the algebraic structure of a finite semigroup $S$ that is determined by its associated upper non-nilpotent graph $\mathcal{N}_{S}$. The vertices of this graph are the elements of $S$ and two…
Jacobson proved that if a Lie algebra admits an invertible derivation, it must be nilpotent. He also suspected, though incorrectly, that the converse might be true: that every nilpotent Lie algebra has an invertible derivation. We prove…
In the present paper we give the full description of the Lie nilpotent group algebras which have maximal Lie nilpotency indices.
We classify nilpotent Lie algebras with complex structures of weakly non-nilpotent type in real dimension eight, which is the lowest dimension where they arise. Our study, together with previous results on strongly non-nilpotent structures,…
In general, the study of gradations has always represented a cornerstone in algebra theory. In particular, \textit{naturally graded} seems to be the first and the most relevant gradation when it comes to nilpotent algebras, a large class of…
We present a functorial construction which, starting from a congruence $\alpha$ of finite index in an algebra A, yields a new algebra C with the following properties: the congruence lattice of C is isomorphic to the interval of congruences…
We study the algebraic constraints on the structure of nilpotent Lie algebra $\mathbb{g}$, which arise because of the presence of an integrable complex structure $J$. Particular attention is paid to non-abelian complex structures.…
A basic fact taught in undergraduate algebra courses is that every finite nilpotent group is a direct product of $p$-groups. Already Bruck observed that this does not generalize to loops. In particular, there exist nilpotent loops of size…
The extending structures and unified products for Malcev algebras are developed. Some special cases of unified products such as crossed products and matched pair of Malcev algebras are studied. It is proved that the extending structures can…
In this paper, we determine the structure of the nilpotent multipliers of all pairs $(G,N)$ of finitely generated abelian groups where $N$ admits a complement in $G$. Moreover, some inequalities for the nilpotent multipliers of pairs of…
We prove that the class of nilpotent by finite, solvable by finite, polycyclic by finite, nilpotent of nilpotency class $n$ and supersolvable groups are closed under the formation of the non-abelian tensor product. We provide necessary and…
We present some results, both rigorously mathematical and computational, showing unexpected relations between different identities expressing nilpotence in nonassociative algebras, and formulate a number of conjectural generalizations and…