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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Malcev algebras with $ J\sb{2}$-potent radical

Author: Ernest L. Stitzinger
Journal: Proc. Amer. Math. Soc. 50 (1975), 1-9
MSC: Primary 17E05
MathSciNet review: 0374224
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Abstract: Let $ A$ be a Malcev algebra, $ B$ be an ideal of $ A$ and $ J_2^1(B) = J(B,A,A)$ where $ J(B,A,A)$ is the linear subspace of $ A$ spanned by all elements of the form $ J(x,y,z) = (xy)z + (yz)x + (zx)y,x \in B,y,z \in A$. For $ k \geq 1$, define $ J_2^{k + 1}(B) = J(J_2^k(B),A,A)$. Then $ B$ is called $ {J_2}$-potent if there exists an integer $ N \geq 1$ such that $ J_2^N(B) = 0$. Now let $ A$ be a Malcev algebra over a field of characteristic 0 such that the radical $ R$ of $ A$ is $ {J_2}$-potent. Then $ R$ is complemented by a semisimple subalgebra and all such complements are strictly conjugate in $ A$. The proofs follow those in the Lie algebra case.

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Article copyright: © Copyright 1975 American Mathematical Society