Anti-commuting varieties
نویسندگان
چکیده
منابع مشابه
Irregular and Singular Loci of Commuting Varieties
Let C be the commuting variety of the Lie algebra g of a connected noncommutative reductive algebraic group G over an algebraically closed field of characteristic zero. Let C be the singular locus of C and let C be the locus of points whose G-stabilizers have dimension > rk G. We prove that: (a) C is a nonempty subset of C; (b) codimCC irr = 5−max l(a) where the maximum is taken over all simple...
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We prove a formula, originally due to Feit and Fine, for the class of the commuting variety in the Grothendieck group of varieties. Our method, which uses a power structure on the Grothendieck group of stacks, allows us to prove several refinements and generalizations of the Feit-Fine formula. Our main application is to motivic DonaldsonThomas theory.
متن کاملCommuting Pairs and Triples of Matrices and Related Varieties
In this note, we show that the set of all commuting d-tuples of commuting n × n matrices that are contained is an n-dimensional commutative algebra is a closed set, and therefore, Gerstenhaber’s theorem on commuting pairs of matrices is a consequence of the irreducibility of the variety of commuting pairs. We show that the variety of commuting triples of 4×4 matrices is irreducible. We also stu...
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The ground field k is algebraically closed and of characteristic zero. Let g be a reductive algebraic Lie algebra over k and σ an involutory automorphism of g. Then g = g0 ⊕ g1 is the direct sum of σ-eigenspaces. Here g0 is a reductive subalgebra and g1 is a g0-module. Let G be the adjoint group of g and G0 ⊂ G a connected subgroup with LieG0 = g0. The commuting variety of (g, g0) is the follow...
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ژورنال
عنوان ژورنال: Transactions of the American Mathematical Society
سال: 2019
ISSN: 0002-9947,1088-6850
DOI: 10.1090/tran/8017