A. Dzhumadil'daev

collaborators

6 papers

math.RA2002

N-commutators on vector fields

A. S. Dzhumadil'daev

An alternating sum of compositions of N vector fields is called N-commutator. In general N-commutator of N vector fields is no longer a vector field. Question: is it possible to fi…

math.RA2002

Wronskians as n-Lie multiplications

A. S. Dzhumadil'daev

Filipov proved that Jacobian algebra is n-Lie. In our paper we consider algebras defined on associative commutative algebra U with derivation $\der$ by (k+1)-multiplication $V^{0,1…

math.RT2002

Representations of n-Lie algebras

A. S. Dzhumadil'daev

Let $V_{n} =< e_{1}, ..., e_{n + 1} >$ be a vector products n-Lie algebra with n-Lie commutator $[e_{1}, ..., e_{i}^, ..., e_{n + 1}] = (- 1)^{i} e_{i}$ over the field of complex numbers. Any finite-dimen…

math.RA2002

Identities and derivations for Jacobian algebras

A. S. Dzhumadil'daev

Constructions of n-Lie algebras by strong n-Lie-Poisson algebras are given. First cohomology groups of adjoint module of Jacobian algebras are calculated. Minimal identities of 3-J…

math.RT1998

Minimal polynomial identities for right-symmetric algebras

Askar Dzhumadil'daev

An algebra $A$ with multiplication $A \times A \to A, (a, b) \mapsto a \circ b$ , is called right-symmetric, if $a \circ (b \circ c) - (a \circ b) \circ a \circ (c \circ b) - (a \circ c) \circ b,$ f…

math.DG1998

Cohomologies and deformations of right-symmetric algebras

Askar Dzhumadil'daev

An algebra $A$ with identity $(a \circ b) \circ c - a \circ (b \circ c) = (a \circ c) \circ b - a \circ (c \circ b),$ is called right-symmetric. Cohomology and deformation theory for right-symmetr…