共查询到20条相似文献,搜索用时 187 毫秒
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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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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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Tathagata Basak 《Journal of Pure and Applied Algebra》2018,222(10):3036-3042
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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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Tim Seynnaeve 《Comptes Rendus Mathematique》2018,356(1):52-55
Motivated by the symmetric version of matrix multiplication we study the plethysm of the adjoint representation of the Lie group . In particular, we describe the decomposition of this representation into irreducible components for , and find highest-weight vectors for all irreducible components. Relations to fast matrix multiplication, in particular the Coppersmith–Winograd tensor, are presented. 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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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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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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Dennis I. Merino 《Linear algebra and its applications》2012,436(7):1960-1968
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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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In this article, we prove that the compact simple Lie groups for , for , for , , and admit left-invariant Einstein metrics that are not geodesic orbit. This gives a positive answer to an open problem recently posed by Nikonorov. 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