Minimal polynomial identities for right-symmetric algebras

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dc.creatorDzhumadil'daev, Askar
dc.date1998-09-16
dc.date.accessioned2026-07-07T05:26:01Z
dc.date.available2026-07-07T05:26:01Z
dc.descriptionAn algebra $A$ with multiplication $A\times A \to A, (a,b)\mapsto a\circ b$, is called right-symmetric, if $a\circ(b\circ c)-(a\circ b)\circ a\circ (c\circ b)-(a\circ c)\circ b,$ for any $a,b,c\in A$. The multiplication of right-symmetric Witt algebras $W_n=\{u\der_i: u\in U, U={\cal K}[x_1^{\pm 1},...,x_n^{\pm}$ or $={\cal K}[x_1,...,x_n], i=1,...,n\}, p=0,$ or $W_n({\bf m)}=\{u\der_i: u\in U, U=O_n({\bf m})\}$, are given by $u\der_i\circ v\der_j=v\der_j(u)\der_i.$ An analogue of the Amitsur-Levitzki theorem for right-symmetric Witt algebras is established. Right-symmetric Witt algebras of $ satisfy the standard right-symmetric identity of degree $2n+1:$ $\sum_{σ\in Sym_{2n}}sign(σ)a_{σ(1)}\circ(a_{σ(2)}\circ >...(a_{σ(2n)}\circ a_{2n+1})...)=0.$ The minimal deg$ left polynomial identities of $W_n^{rsym}, W_n^{+rsym}, p=0,$ i$ The minimal degree of multilinear left polynomial identity of $$ is also $2n+1.$ All left polynomial (also multilinear, if $p>0$) identities of right-symmetric Witt algebras of minimal $ combinations of left polynomials obtained from standard ones by permutations of arguments.
dc.description20 pages, latex, no figures
dc.identifierhttps://arxiv.org/abs/math/9809082
dc.identifierhttp://arxiv.org/abs/math/9809082
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/77402
dc.subjectRepresentation Theory
dc.subjectRings and Algebras
dc.titleMinimal polynomial identities for right-symmetric algebras
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