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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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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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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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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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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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Laura Geatti 《Differential Geometry and its Applications》2012,30(2):195-205
We consider the action of a real semisimple Lie group G on the complexification of a semisimple symmetric space and we present a refinement of Matsuki?s results (Matsuki, 1997 [1]) in this case. We exhibit a finite set of points in , sitting on closed G-orbits of locally minimal dimension, whose slice representation determines the G-orbit structure of . Every such point lies on a compact torus and occurs at specific values of the restricted roots of the symmetric pair . The slice representation at is equivalent to the isotropy representation of a real reductive symmetric space, namely . In principle, this gives the possibility to explicitly parametrize all G-orbits in . 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
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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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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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Let V be an n-dimensional vector space over the finite field consisting of q elements and let be the Grassmann graph formed by k-dimensional subspaces of V, . Denote by the restriction of to the set of all non-degenerate linear codes. We show that for any two codes the distance in coincides with the distance in only in the case when , i.e. if n is sufficiently large then for some pairs of codes the distances in the graphs and are distinct. We describe one class of such pairs. 相似文献
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John Bamberg S.P. Glasby Luke Morgan Alice C. Niemeyer 《Journal of Pure and Applied Algebra》2018,222(10):2931-2951
Let be a prime. For each maximal subgroup with , we construct a d-generator finite p-group G with the property that induces H on the Frattini quotient and . A significant feature of this construction is that is very small compared to , shedding new light upon a celebrated result of Bryant and Kovács. The groups G that we exhibit have exponent p, and of all such groups G with the desired action of H on , the construction yields groups with smallest nilpotency class, and in most cases, the smallest order. 相似文献