On Complex Lie Supergroups and Homogeneous Split Supermanifolds

Vishnyakova, Elizaveta

doi:10.48550/arxiv.0908.1164

Cited by 7 publications

(11 citation statements)

References 10 publications

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“…The existence of such groups in the differential and analytic categories is granted through the theory of Harish-Chandra pairs, in which the category of supergroups is identified with pairs consisting of a Lie group and a super Lie algebra, (see [22], [2] and [31] for more details on this subject). Our theory allows to realize such supergroups explicitly and over arbitrary fields.…”

Section: Chevalley Supergroups As Algebraic Supergroups67mentioning

confidence: 99%

“…Another immediate consequence of Corollary 5.3.10 and Proposition 5.3.12 is the following, which improves, for Chevalley supergroups, a more general result proved by Masuoka (cf. [25], Theorem 4.5) in the algebraic-supergeometry setting (see also [31], and references therein, for the complex-analytic case).…”

Section: Chevalley Supergroups As Algebraic Supergroups67mentioning

confidence: 99%

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Chevalley supergroups

2012

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In the framework of algebraic supergeometry, we give a construction\ud of the scheme-theoretic supergeometric analogue of Chevalley groups, namely affine algebraic supergroups associated to simple Lie superalgebras of classical type. This provides a unified approach to most of the algebraic supergroups considered so far in literature, and an effective method to construct new ones. As an intermediate step, we prove an existence theorem for Chevalley bases of simple classical\ud Lie superalgebras and a PBW-like theorem for their associated\ud Kostant superalgebras

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Section: Chevalley Supergroups As Algebraic Supergroups67mentioning

confidence: 99%

Section: Chevalley Supergroups As Algebraic Supergroups67mentioning

confidence: 99%

Chevalley supergroups

2012

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“…In the complex case, the equivalence of the categories was shown in [18]. If a Harish-Chandra pair (G, g) is given, it determines the Lie supergroup (G, O G ) in the following way, see [8].…”

Section: The Harish-chandra Pairsmentioning

confidence: 99%

“…h0 = Lie H and α H = α G |H. There is a correspondence between Harish-Chandra subpairs of (G, g) and Lie subsupergroups of (G, O G ), see, e.g., [18]. (The Lie supergroup (G, O G ) corresponds to the Harish-Chandra pair (G, g).…”

Section: The Harish-chandra Pairsmentioning

confidence: 99%

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On holomorphic functions on a compact complex homogeneous supermanifold

Vishnyakova

2012

Journal of Algebra

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It is well-known that non-constant holomorphic functions do not exist on a compact complex manifold. This statement is false for a supermanifold with a compact reduction. In this paper we study the question under what conditions non-constant holomorphic functions do not exist on a compact homogeneous complex supermanifold. We describe also the vector bundles determined by split homogeneous complex supermanifolds. As an application, we compute the algebra of holomorphic functions on the classical flag supermanifolds which were introduced by Yu.I. Manin.Comment: 29 page

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The Harish-Chandra isomorphism for reductive symmetric superpairs

Alldridge

2012

Transformation Groups

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We consider symmetric pairs of Lie superalgebras which are strongly reductive and of even type, and introduce a graded Harish-Chandra homomorphism. We prove that its image is a certain explicit filtered subalgebra of the Weyl invariants on a Cartan subspace whose associated graded is the image of Chevalley's restriction map on symmetric invariants. This generalises results of Harish-Chandra and V. Kac, M. Gorelik.Comment: 43 pages; v2: substantially improved versio

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On Complex Lie Supergroups and Homogeneous Split Supermanifolds

Cited by 7 publications

References 10 publications

Chevalley supergroups

Chevalley supergroups

On holomorphic functions on a compact complex homogeneous supermanifold

The Harish-Chandra isomorphism for reductive symmetric superpairs

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