The R-Matrix Presentation for the Yangian of a Simple Lie Algebra
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DOI: 10.1007/s00220-018-3227-4
Abstract: Starting from a finite-dimensional representation of the Yangian $${Y (\mathfrak{g})}$$Y(g) for a simple Lie algebra $$ \mathfrak{g}$$g in Drinfeld’s original presentation, we construct a Hopf algebra $${{X}_\mathcal{I}(\mathfrak{g})}$$XI(g), called the extended Yangian, whose defining relations are… read more here.
Keywords: algebra; lie; matrix; simple lie ... See more keywords
Geodesic orbit metrics on compact simple Lie groups arising from flag manifolds
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DOI: 10.1016/j.crma.2018.06.004
Abstract: Abstract In this paper, we investigate left-invariant geodesic orbit metrics on connected simple Lie groups, where the metrics are formed by the structures of flag manifolds. We prove that all these left-invariant geodesic orbit metrics… read more here.
Keywords: geodesic orbit; simple lie; flag manifolds; lie groups ... See more keywords
Singular vector formulas for Verma modules of simple Lie superalgebras
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DOI: 10.1016/j.jalgebra.2018.11.028
Abstract: Abstract For a simple Lie superalgebra of type BDFG, we give explicit formulas for singular vectors in a Verma module of highest weight λ − ρ , which have weight s γ λ − ρ… read more here.
Keywords: verma modules; modules simple; simple lie; singular vector ... See more keywords
Restricted one-dimensional central extensions of restricted simple Lie algebras
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DOI: 10.1016/j.laa.2016.09.037
Abstract: Abstract We study the restricted one-dimensional central extensions of an arbitrary finite dimensional restricted simple Lie algebra for p ≥ 5 . For H 2 ( g ) = 0 , we explicitly describe the… read more here.
Keywords: central extensions; restricted simple; one dimensional; simple lie ... See more keywords