On the Lie structure of a prime associative superalgebra

2013/07/11 by Jesus Laliena, Laliena, Jesus
Mathematics · #16W55 #17A70 #17C70 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16W55 #msc:17A70 #msc:17C70

paper · pdf · doi:10.48550/arxiv.1307.3243

arxiv created 2013/07/11 · arxiv updated 2013/07/15

Abstract

In this paper some results on the Lie structure of prime superalgebras are discussed. We prove that, with the exception of some special cases, for a prime superalgebra, A, over a ring of scalars Φ with 1/2∈ Φ, if L is a Lie ideal of A and W is a subalgebra of A such that [W, L]⊆ W, then either L⊆ Z or W⊆ Z. Likewise, if V is a submodule of A and [V, L]⊆ V, then either V⊆ Z or L⊆ Z or there exists an ideal of A, M, such that 0\not= [M,A]⊆ V. This work extends to prime superalgebras some results of I. N. Herstein, C. Lanski and S. Montgomery on prime algebras.

Related

• Lie structure in semiprime superalgebrs with superinvolution
• Lie Superautomorphisms on Associative Algebras, II
• The derived superalgebra of skew elements of a semiprime superalgebra with superinvolution
• Prime ideals in C*-algebras and applications to Lie theory
• Maximal subalgebras and chief factors of Lie algebras