共查询到20条相似文献,搜索用时 15 毫秒
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Adrien Deloro 《代数通讯》2013,41(5):1981-2008
We identify the spaces of homogeneous polynomials in two variables 𝕂[Yk, XYk?1, ?, Xk] among representations of the Lie ring 𝔰𝔩2(𝕂). This amounts to constructing a compatible 𝕂-linear structure on some abstract 𝔰𝔩2(𝕂)-modules, where 𝔰𝔩2(𝕂) is viewed as a Lie ring. 相似文献
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The universal central extensions and their extension kernels of the smatrix Lie superalgebra 𝔰𝔩(m, n, 𝒜), the Steinberg Lie superalgebra 𝔰𝔩(m, n, 𝒜) in category SLeib of Leibniz superalgebras are determined under a weak assumption (compared with Mikhalev and Pinchuk, 2000) using the first Hochschild homology and the first cyclic homology group. 相似文献
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Whereas Holm proved that the ring of differential operators on a generic hyperplane arrangement is finitely generated as an algebra, the problem of its Noetherian properties is still open. In this article, after proving that the ring of differential operators on a central arrangement is right Noetherian if and only if it is left Noetherian, we prove that the ring of differential operators on a central 2-arrangement is Noetherian. In addition, we prove that its graded ring associated to the order filtration is not Noetherian when the number of the consistuent hyperplanes is greater than 1. 相似文献
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The finite-dimensional simple modules over the Drinfeld double of the bosonization of the Nichols algebra 𝔲𝔣𝔬(7) are classified. 相似文献
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Brett D. Wick 《Mathematische Nachrichten》2009,282(6):912-916
It is shown that for A?(??) functions f1 and f2 with and f1 being positive on real zeros of f2 then there exists A?(??) functions g2 and g1, g1–1 with and This result is connected to the computation of the stable rank of the algebra A?(??) and to Control Theory (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Based on the works of Du and Gu, the canonical bases of U(𝔤𝔩3|1) are completely determined in this paper. 相似文献
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We study a family of complex representations of the group GL n (𝔬), where 𝔬 is the ring of integers of a non-archimedean local field F. These representations occur in the restriction of the Grassmann representation of GL n (F) to its maximal compact subgroup GL n (𝔬). We compute explicitly the transition matrix between a geometric basis of the Hecke algebra associated with the representation and an algebraic basis that consists of its minimal idempotents. The transition matrix involves combinatorial invariants of lattices of submodules of finite 𝔬-modules. The idempotents are p-adic analogs of the multivariable Jacobi polynomials. 相似文献
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Donald W. Barnes 《代数通讯》2013,41(4):1170-1171
Let 𝔉 be a saturated formation of soluble Lie algebras. Let L be a soluble Lie algebra, and let U be an 𝔉-normalizer of L. Then U is intravariant in L. 相似文献
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Orthogonal decomposition of the special linear Lie algebra over the complex numbers was studied in the early 1980s and attracted further attentions in the past decade due to its application in quantum information theory. In this paper, we study this decomposition problem of the special linear Lie algebra over a finite commutative ring with identity. 相似文献
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We give a generalization of the Stone–Weierstrass property for subalgebras of C (X), with X a completely regular Hausdorff space. In particular, we study in this paper some subalgebras of C0(X), with X a locally compact Hausdorff space, provided with weighted norm topology. By using the Stone–Weierstrass property, we then describe the ideal structure of these algebras. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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Let R be a commutative ring with identity. The set 𝕀(R) of all ideals of R is a bounded semiring with respect to ordinary addition, multiplication and inclusion of ideals. The zero-divisor graph of 𝕀(R) is called the annihilating-ideal graph of R, denoted by 𝔸𝔾(R). We write 𝒢 for the set of graphs whose cores consist of only triangles. In this paper, the types of the graphs in 𝒢 that can be realized as either the zero-divisor graphs of bounded semirings or the annihilating-ideal graphs of commutative rings are determined. A necessary and sufficient condition for a ring R such that 𝔸𝔾(R) ∈ 𝒢 is given. Finally, a complete characterization in terms of quotients of polynomial rings is established for finite rings R with 𝔸𝔾(R) ∈ 𝒢. Also, a connection between finite rings and their corresponding graphs is realized. 相似文献
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