The Experts below are selected from a list of 258 Experts worldwide ranked by ideXlab platform
Anna Melnikov - One of the best experts on this subject based on the ideXlab platform.
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On varieties in an orbital variety closure in Semisimple Lie Algebras
Journal of Algebra, 2020Co-Authors: Anna MelnikovAbstract:Abstract In this note we discuss the closure of an orbital variety as a union of varieties. We show that if Semisimple Lie Algebra g contains factors not of type A n then there are orbital varieties whose closure contains components which are not Lagrangian. We show that the argument does not work if all the factors are of type A n and provide the facts supporting the conjecture claiming that if all the factors of g are of type A n then the closure of an orbital variety is a union of orbital varieties.
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on varieties in an orbital variety closure in Semisimple Lie Algebra
arXiv: Representation Theory, 2004Co-Authors: Anna MelnikovAbstract:Let g be a Semisimple complex Lie Algebra. Let O be a nilpotent orbit in g. Fix a triangular decomposition g=n+h+n^-. An irreducible component of the intersection of O and n is called an orbital variety associated to O. It is a Lagrangian subvariety of O. In this note we discuss the closure of an orbital variety as a union of varieties. We show that if g contains factors not of type A_n then there are orbital varieties whose closure contains components which are not Lagrangian. We show that the argument does not work if all the factors are of type A_n and provide the facts supporting the conjecture claiming that if all the factors of g are of type A_n then the closure of an orbital variety is a union of orbital varieties.
Mouchira Zaiter - One of the best experts on this subject based on the ideXlab platform.
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on related varieties to the commuting variety of a Semisimple Lie Algebra
Journal of Algebra, 2013Co-Authors: Mouchira ZaiterAbstract:Abstract Let g be a Semisimple Lie Algebra of finite dimension. The nullcone N of g is the set of ( x , y ) in g × g such that x and y are nilpotents and are in the same Borel subAlgebra. The main result of this paper is that N is a closed and irreducible subvariety of g × g and its normalization morphism is bijective.
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on related varieties to the commuting variety of a Semisimple Lie Algebra
arXiv: Representation Theory, 2011Co-Authors: Mouchira ZaiterAbstract:Let g be a Semisimple Lie Algebra of finite dimension. The nullcone N of g is the set of (x,y) in g x g such that x and y are nilpotents and are in the same Borel suAlgebra. The main result of this paper is that N is a closed and irreducible subvariety of g x g, its normalisation has rational singularities and its normalization morphism is bijective.
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on the nullcone and the variety chi_ mathfrak g of a Semisimple Lie Algebra
arXiv: Representation Theory, 2010Co-Authors: Mouchira ZaiterAbstract:Let g be a Semisimple Lie Algebra of finite dimension. The nullcone N of g is the set of (x, y) in g\timesg such that x and y are nilpotents and are in the same Borel subAlgebra. The main result of this paper is that N is a closed and irreducible subvariety of g \times g whose normalization has rational singularities and such that the normalization morphism is bijective.
R. Zegers - One of the best experts on this subject based on the ideXlab platform.
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Deformation Quasi-Hopf Algebras of Non-Semisimple Type from Cochain Twists
Communications in Mathematical Physics, 2010Co-Authors: C. A. S. Young, R. ZegersAbstract:Given a symmetric decomposition $${\mathfrak g=\mathfrak h\oplus \mathfrak p}$$ of a Semisimple Lie Algebra $${\mathfrak g}$$ , we define the notion of a $${\mathfrak p}$$ -contractible quantized universal enveloping Algebra (QUEA): for these QUEAs the contraction $${\mathfrak g\rightarrow\mathfrak g_0}$$ making $${\mathfrak p}$$ abelian is nonsingular and yields a QUEA of $${\mathfrak g_0}$$ . For a certain class of symmetric decompositions, we prove, by refining cohomological arguments due to Drinfel’d, that every QUEA of $${\mathfrak g_0}$$ so obtained is isomorphic to a cochain twist of the undeformed envelope $${\mathcal U(\mathfrak g_0)}$$ . To do so we introduce the $${\mathfrak p}$$ -contractible Chevalley-Eilenberg complex and prove, for this class of symmetric decompositions, a version of Whitehead’s lemma for this complex. By virtue of the existence of the cochain twist, there exist triangular quasi-Hopf Algebras based on these contracted QUEAs and, in the approach due to Beggs and Majid, the dual quantized coordinate Algebras admit quasi-associative differential calculi of classical dimensions. As examples, we consider κ -Poincaré in 3 and 4 spacetime dimensions.
Apoorva Khare - One of the best experts on this subject based on the ideXlab platform.
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weights of simple highest weight modules over a complex Semisimple Lie Algebra
arXiv: Representation Theory, 2013Co-Authors: Apoorva KhareAbstract:In this short note we announce three formulas for the set of weights of various classes of highest weight modules $\V$ with highest weight \lambda, over a complex Semisimple Lie Algebra $\Lie{g}$ with Cartan subAlgebra $\Lie{h}$. These include, but are not restricted to, all (highest weight) simple modules L(\lambda). We also assert that these formulas are the "best possible", in that they do not hold in general for other highest weight modules in a very precise sense. The proofs of the results in this note are included in an updated copy (Version 3) of the paper arxiv:1301.1140 . The proofs involve studying the convex hull of the set of $\Lie{h}$-weights $\wt(\V)$ in their own right. Thus, we show that if $\V = L(\lambda)$ is simple, or if \lambda\ is not on a simple root hyperplane and $\V$ is arbitrary, the hull of the infinite set $\wt(\V)$ is a convex polyhedron - i.e., cut out by only finitely many hyperplanes. (This extends the notion of the Weyl polytope to arbitrary simple modules L(\lambda).) It is also shown that the partially ordered set (under quotienting) of modules $\V$ with fixed convex hull, has unique "largest" and "smallest" elements.
Polyxeni Lamprou - One of the best experts on this subject based on the ideXlab platform.
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slices for maximal parabolic subAlgebras of a Semisimple Lie Algebra
Transformation Groups, 2017Co-Authors: Florence Fauquantmillet, Polyxeni LamprouAbstract:Let p denote a maximal (truncated) parabolic subAlgebra of a simple Lie Algebra \( \mathfrak{g} \). It is known that the Poisson centre Y (\( \mathfrak{p} \)) is a polynomial Algebra in many cases. We construct a slice for the coadjoint action of p, thus extending a theorem of Kostant. The role of the principal \( \mathfrak{s}\mathfrak{l} \) 2-triple is played by an adapted pair.
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slices for maximal parabolic subAlgebras of a Semisimple Lie Algebra
arXiv: Representation Theory, 2015Co-Authors: Florence Fauquantmillet, Polyxeni LamprouAbstract:Let p be a maximal truncated parabolic subAlgebra of a simple Lie Algebra. It was shown in many cases that the Poisson centre Y(p) is a polynomial Algebra. We construct a slice for the coadjoint action of p, thus extending a theorem of Kostant. The role of the principal sl_2-triple is played by an adapted pair.
