Let Mn be the algebra of all n × n complex matrices and gl（n, C） be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ ： gl（n, C） → gl（n, C） preserves solvability in both directions...Let Mn be the algebra of all n × n complex matrices and gl（n, C） be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ ： gl（n, C） → gl（n, C） preserves solvability in both directions if both φ and φ-1 map every solvable Lie subalgebra of gl（n, C） to some solvable Lie subalgebra. In this paper we classify the invertible linear maps preserving solvability on gl（n, C） in both directions. As a sequence, such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.展开更多
Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if ...Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if it maps every staircase subalgebra to some staircase subalgebra of the same dimension. In this paper, we devote to giving an explicit description on the invertible maps on g that preserve staircase subalgebras.展开更多
基金The NSF (2009J05005) of Fujian Provincea Key Project of Fujian Provincial Universities-Information Technology Research Based on Mathematics
文摘Let Mn be the algebra of all n × n complex matrices and gl（n, C） be the general linear Lie algebra, where n ≥ 2. An invertible linear map φ ： gl（n, C） → gl（n, C） preserves solvability in both directions if both φ and φ-1 map every solvable Lie subalgebra of gl（n, C） to some solvable Lie subalgebra. In this paper we classify the invertible linear maps preserving solvability on gl（n, C） in both directions. As a sequence, such maps coincide with the invertible linear maps preserving commutativity on Mn in both directions.
基金The NSF (11126121) of ChinaPh.D.Fund (B2010-93) of Henan Polytechnic University+1 种基金Natural Science Research Program (112300410120) of Science and Technology Department of Henan ProvinceNatural Science Research Program (2011B110016) of Education Department of Henan Province
文摘Let g be the general linear Lie algebra consisting of all n x n matrices over a field F and with the usual bracket operation {x, y} =xy - yx. An invertible map φ ： g →g is said to preserve staircase subalgebras if it maps every staircase subalgebra to some staircase subalgebra of the same dimension. In this paper, we devote to giving an explicit description on the invertible maps on g that preserve staircase subalgebras.
