科研之友
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摘要
Fix an infinite set I and consider the associative matrix algebra M-I(F) where F is a base field with char(F) not equal 2. For any couple of bijective maps sigma, nu : I -> I, such that sigma nu = nu sigma and sigma(2) = nu(2), we introduce a linear subspace Omega(sigma, nu) of M-I(F). We endow it with a structure of (non-associative) algebra for a certain bilinear product, and obtain a wide class of non associative algebras containing, in particular, the Lie algebras Lie(M-I(F), t). We show that each algebra Omega(sigma, nu) is simple.
- 出版日期2017-9-1
