This article is cited in 6 papers

Commutator identities of the homotopes of $(-1,1)$-algebras

S. V. Pchelintsev

Finance Academy of the Government of the Russian Federation, Moscow, Russia

Abstract: We study the commutator algebras of the homotopes of $(-1,1)$-algebras and prove that they are Malcev algebras satisfying the Filippov identity $h_\alpha(x,y,z)=0$ in the case of strictly $(-1,1)$-algebras. We also proved that every Malcev algebra with the identities $xy^3=0$, $xy^2z^2=0$ and $h_\alpha(x,y,z)=0$ is nilpotent of index at most 6.

Keywords: $(-1,1)$-algebra, Malcev algebra, homotope, identity, Filippov functions, nilpotency.

UDC: 512.554

Received: 07.12.2011

 English version: Siberian Mathematical Journal, 2013, 54:2, 325–340

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