LINEAR FAMILY OF LIE BRACKETS ON THE SPACE OF MATRICES Mat(n×m,K) AND ADO’S THEOREM
نویسنده
چکیده
Abstract. In this paper we classify a linear family of Lie brackets on the space of rectangular matrices Mat(n×m, K) and we give an analogue of the Ado’s Theorem. We give also a similar classification on the algebra of the square matrices Mat(n, K) and as a consequence, we prove that we can’t built a faithful representation of the (2n + 1)-dimensional Heisenberg Lie algebra Hn in a vector space V with dimV ≤ n+1. Finally, we prove that in the case of the algebra of square matrices Mat(n, K), the corresponding Lie algebras structures are a contraction of the canonical Lie algebra gl(n, K).
منابع مشابه
LINEAR FAMILY OF LIE BRACKETS ON THE SPACE OF MATRICES Mat(n×m,K) AND ADO’S THEOREM
Abstract. In this paper we classify a linear family of Lie brackets on the space of rectangular matrices Mat(n×m, K) and we give an analogue of the Ado’s Theorem. We give also a similar classification on the algebra of the square matrices Mat(n, K) and as a consequence, we prove that we can’t built a faithful representation of the (2n + 1)-dimensional Heisenberg Lie algebra Hn in a vector space...
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