共查询到20条相似文献,搜索用时 46 毫秒
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In this paper we determine the projective unitary representations of finite dimensional Lie supergroups whose underlying Lie superalgebra is , where is a compact simple Lie superalgebra and A is a supercommutative associative (super)algebra; the crucial case is when is a Graßmann algebra. Since we are interested in projective representations, the first step consists in determining the cocycles defining the corresponding central extensions. Our second main result asserts that, if is a simple compact Lie superalgebra with , then each (projective) unitary representation of factors through a (projective) unitary representation of itself, and these are known by Jakobsen's classification. If , then we likewise reduce the classification problem to semidirect products of compact Lie groups K with a Clifford–Lie supergroup which has been studied by Carmeli, Cassinelli, Toigo and Varadarajan. 相似文献
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Anton Alekseev Nariya Kawazumi Yusuke Kuno Florian Naef 《Comptes Rendus Mathematique》2017,355(2):123-127
We define a family of Kashiwara–Vergne problems associated with compact connected oriented 2-manifolds of genus g with boundary components. The problem is the classical Kashiwara–Vergne problem from Lie theory. We show the existence of solutions to for arbitrary g and n. The key point is the solution to based on the results by B. Enriquez on elliptic associators. Our construction is motivated by applications to the formality problem for the Goldman–Turaev Lie bialgebra . In more detail, we show that every solution to induces a Lie bialgebra isomorphism between and its associated graded . For , a similar result was obtained by G. Massuyeau using the Kontsevich integral. For , , our results imply that the obstruction to surjectivity of the Johnson homomorphism provided by the Turaev cobracket is equivalent to the Enomoto–Satoh obstruction. 相似文献
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We classify the 6-dimensional Lie algebras of the form that admit an integrable complex structure. We also endow a Lie algebra of the kind () with such a complex structure. The motivation comes from geometric structures à la Sasaki on -manifolds. 相似文献
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Dave Anderson Mathieu Florence Zinovy Reichstein 《Comptes Rendus Mathematique》2013,351(23-24):871-875
Let G be a split simple group of type over a field k, and let be its Lie algebra. Answering a question of J.-L. Colliot-Thélène, B. Kunyavski?, V.L. Popov, and Z. Reichstein, we show that the function field is generated by algebraically independent elements over the field of adjoint invariants . 相似文献
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Cyril Lacoste 《Comptes Rendus Mathematique》2018,356(2):141-145
We prove that the set of symplectic lattices in the Siegel space whose systoles generate a subspace of dimension at least 3 in does not contain any -equivariant deformation retract of . 相似文献
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We present a simple no-go theorem for the existence of a deformation quantization of a homogeneous space M induced by a Drinfel'd twist: we argue that equivariant line bundles on M with non-trivial Chern class and symplectic twist star products cannot both exist on the same manifold M. This implies, for example, that there is no symplectic star product on the projective space induced by a twist based on or any sub-bialgebra, for every . 相似文献
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With any -manifold M are associated two dglas and , whose cohomologies and are Gerstenhaber algebras. We establish a formality theorem for -manifolds: there exists an quasi-isomorphism whose first ‘Taylor coefficient’ (1) is equal to the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd cocycle of the -manifold M, and (2) induces an isomorphism of Gerstenhaber algebras on the level of cohomology. Consequently, the Hochschild–Kostant–Rosenberg map twisted by the square root of the Todd class of the -manifold M is an isomorphism of Gerstenhaber algebras from to . 相似文献
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Houssein El Turkey 《Journal of Pure and Applied Algebra》2018,222(1):181-190
The complexity of a module is the rate of growth of the minimal projective resolution of the module while the z-complexity is the rate of growth of the number of indecomposable summands at each step in the resolution. Let () be the type II orthosymplectic Lie superalgebra of types B or D. In this paper, we compute the complexity and the z-complexity of the simple finite-dimensional -supermodules. We then give these complexities certain geometric interpretations using support and associated varieties. 相似文献
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Pham Hung Quy 《Journal of Pure and Applied Algebra》2018,222(5):1126-1138
Let be an equidimensional excellent local ring of characteristic . The aim of this paper is to show that does not depend on the choice of parameter ideal provided R is an F-injective local ring that is F-rational on the punctured spectrum. 相似文献
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Jarnishs Beltran Marco Farinati Enrique G. Reyes 《Journal of Pure and Applied Algebra》2018,222(8):2006-2021
We describe the space of central extensions of the associative algebra of formal pseudo-differential symbols in independent variables using Hochschild (co)homology groups: we prove that the first Hochschild (co)homology group is 2n-dimensional and we use this fact to calculate the first Lie (co)homology group of equipped with the Lie bracket induced by its associative algebra structure. As an application, we use our calculations to provide examples of infinite-dimensional quadratic symplectic Lie algebras. 相似文献
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Let G be a complex linear algebraic group, its Lie algebra and a nilpotent element. Vust's Theorem says that in case of , the algebra , where is the stabilizer of e under the adjoint action, is generated by the image of the natural action of d-th symmetric group and the linear maps . In this paper, we give an analogue of Vust's Theorem for and when the nilpotent elements e satisfy that is normal. As an application, we study the higher Schur–Weyl duality in the sense of [4] for types B, C and D, which establishes a relationship between W-algebras and degenerate affine braid algebras. 相似文献
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Gábor Korchmáros Maria Montanucci Pietro Speziali 《Journal of Pure and Applied Algebra》2018,222(7):1810-1826
Let be the algebraic closure of a finite field of odd characteristic p. For a positive integer m prime to p, let be the transcendence degree 1 function field defined by . Let and . The extension is a non-Galois extension. Let K be the Galois closure of F with respect to H. By Stichtenoth [20], K has genus , p-rank (Hasse–Witt invariant) and a -automorphism group of order at least . In this paper we prove that this subgroup is the full -automorphism group of K; more precisely where Δ is an elementary abelian p-group of order and D has an index 2 cyclic subgroup of order . In particular, , and if K is ordinary (i.e. ) then . On the other hand, if G is a solvable subgroup of the -automorphism group of an ordinary, transcendence degree 1 function field L of genus defined over , then ; see [15]. This shows that K hits this bound up to the constant .Since has several subgroups, the fixed subfield of such a subgroup N may happen to have many automorphisms provided that the normalizer of N in is large enough. This possibility is worked out for subgroups of Δ. 相似文献