Related papers: Higher Jacobi identities

In 1957, Nemytskii proved the following fact: if in a locally compact or in an Abelian connected group there is a neighborhood of the identity in which some identity holds, then it holds in the entire group. The following question was also…

Working over an arbitrary field of characteristic different from $2$, we extend the Skjelbred-Sund method to compatible Lie algebras and give a full classification of nilpotent compatible Lie algebras up to dimension $4$. In case the base…

We study solvable Lie algebras in prime characteristic $p$ that admit non-singular derivations. We show that Jacobson's Theorem remains true if the quotients of the derived series have dimension less than~$p$. We also study the structure of…

For a prime p and natural number n with p greater than or equal to n, we establish the existence of a non-functorial one-to-one correspondence between isomorphism classes of groups of order p^n whose derived subgroup has exponent dividing…

We address the problem of admissibility of pre-Lie structures associated with a given Lie algebra, particularly, semisimple Lie algebras over ${\mathbb C}$. Such structures are collectively referred to as Lie-admissible algebras, which are…

We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions. The updated version corrects some of the arguments made in Sections 4.5 - 4.7. The statements of…

On the set H_n(K) of symmetric n by n matrices over the field K we can define various binary and ternary products which endow it with the structure of a Jordan algebra or a Lie or Jordan triple system. All these non-associative structures…

We consider two different constructions of higher brackets. First, based on a Grassmann-odd, nilpotent \Delta operator, we define a non-commutative generalization of the higher Koszul brackets, which are used in a generalized…

In this paper, we first introduce the concept of symmetric biderivation radicals and characteristic subalgebras of Lie algebras, and study their properties. Based on these results, we precisely determine biderivations of some Lie algebras…

A symmetry $SU(2,2)$ group in terms of ladder operators is presented for the Jacobi polynomials, $J_{n}^{(\alpha,\beta)}(x)$, and the Wigner $d_j$-matrices where the spins $j=n+(\alpha+\beta)/2$ integer and half-integer are considered…

Continuous groups of the form: $G+a_0G$ are defined, where $G$ denotes a Lie group and $a_0$ denotes an antilinear operation which fullfils the condition $a^2_0=\pm 1$. The matrix algebras connected with the groups $G+a_0G$ are defined. The…

For an abelian group G we consider braiding in a category of G-graded modules $M^{kG}$ given by a bicharacter \chi on G. For $(G,\chi)$-bialgebra A in $M^{kG}$ an analog of Lie bracket is defined. This bracket is determined by a linear map…

The automorphisms of all 4-dimensional, real Lie Algebras are presented in a comprehensive way. Their action on the space of $4\times 4$, real, symmetric and positive definite, matrices, defines equivalence classes which are used for the…

By direct calculations of matrix form of super Jacobi and mixed super Jacobi identities which are obtained from adjoint representation, and using the automorphism supergroup of the gl(1|1) Lie superalgebra, we determine and classify all…

We study identities of Lie superalgebras over a field of characteristic zero. We construct a series of examples of finite-dimensional solvable Lie superalgebras with a non-nilpotent commutator subalgebra for which PI-exponent of codimension…

In a recent letter, new representations were proposed for the pair of sequences ($\gamma,\delta$), as defined formally by Bailey in his famous lemma. Here we extend and prove this result, providing pairs ($\gamma,\delta$) labelled by the…

Lie superautomorphisms of prime associative superalgebras are considered. A definitive result is obtained for central simple superalgebras: their Lie superautomorphisms are of standard forms, except when the dimension of the superalgebra in…

We classify the N = 1, 2, 3 superconformal Lie algebras of Schwimmer and Seiberg by means of differential non-abelian cohomology, and describe the general philosophy behind this new technique. The structure of the group (functor) of…

We show that whenever \[ [\,\cdot,\cdot]_t = [\,\cdot,\cdot]_0 + t[\,\cdot,\cdot]_1,\qquad \alpha_t = \mathrm{id} + t\alpha_1 \] define an infinitesimal Hom--Lie deformation of $\mathfrak{sl}_2(\mathbb K)$ over $\mathbb K[t]/(t^2)$ and…

We consider polynomial deformations of Lie superalgebras and their representations. For the class A(n-1,0) ~ sl(n/1), we identify families of superalgebras of quadratic and cubic type, consistent with Jacobi identities. For such deformed…