共查询到20条相似文献,搜索用时 78 毫秒
1.
Ivan Kaygorodov 《Linear and Multilinear Algebra》2017,65(6):1142-1157
We construct bases for free unital generalized Poisson superalgebras and for free unital superalgebras of Jordan brackets. Also, we prove an analogue of Farkas’ theorem for PI unital generalized Poisson algebras and PI unital algebras of Jordan brackets. Relations between generic Poisson superalgebras and superalgebras of Jordan brackets are studied. 相似文献
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We classify the central simple finite-dimensional noncommutative Jordan superalgebras of characteristic 0. As a corollary, we describe the Poisson brackets on the simple finite-dimensional Jordan superalgebras of characteristic 0. 相似文献
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Carlo Toffalori 《代数通讯》2013,41(1):331-344
ABSTRACT Representations of simple Jordan superalgebras of Hermitian 3?×?3 matrices over the exceptional simple alternative superalgebras B (1,2) and B (4,2) of characteristic 3 are studied. Every irreducible bimodule over these superalgebras up to isomorphism is either a regular bimodule or its opposite. As corollaries,some analogues of the Kronecker factorization theorem are proved for Jordan superalgebras that contain H3(B (1,2)) and H3(B(4,2)). 相似文献
4.
Alexander S. Stern 《代数通讯》2013,41(5):1815-1823
Irreducible representations of finite dimensional Jordan superalgebras of Poisson brackets over algebraically closed field of zero characteristic are examined. If the number of Grassmann generators n∠4 then such a bimodule is isomorphic to regular bimodule or regular bimodule with opposite eveness of homogeneous elements 相似文献
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We classify the central simple finite-dimensional noncommutative Jordan superalgebras over an algebraically closed field of characteristic . The case of characteristic 0 was considered by the authors in the previous paper [21]. In particular, we describe Leibniz brackets on all finite dimensional central simple Jordan superalgebras except mixed (nor vector neither Poisson) Kantor doubles of the supercommutative superalgebra . 相似文献
8.
Pamela A. Richardson 《代数通讯》2013,41(1):179-207
The centroid of a Jordan superalgebra consists of the natural “superscalar multiplications” on the superalgebra. A philosophical question is whether the natural concept of “scalar” in the category of superalgebras should be that of superscalars or ordinary scalars. Basic examples of Jordan superalgebras are the simple Jordan superalgebras with semisimple even part, which were classified over an algebraically closed field of characteristic ≠ 2 by Racine and Zelmanov. Here, we determine the centroids of the analog of these superalgebras over general rings of scalars and show that they have no odd centroid, suggesting that ordinary scalars are the proper concept. 相似文献
9.
V. G. Skosyrskii 《Algebra and Logic》1994,33(3):169-179
Two new constructions of prime Jordan algebras containing nonzero trivial elements are presented. It is proved that a Jordan superalgebra of Poisson brackets is a homomorphic image of a special one.Translated fromAlgebra i Logika, Vol. 33, No. 3, pp. 301–316, May–June, 1994. 相似文献
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We prove a coordinatization theorem for noncommutative Jordan superalgebras of degree n > 2, describing such algebras. It is shown that the symmetrized Jordan superalgebra for a simple finite-dimensional noncommutative
Jordan superalgebra of characteristic 0 and degree n > 1 is simple. Modulo a “nodal” case, we classify central simple finite-dimensional noncommutative Jordan superalgebras of
characteristic 0. 相似文献
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In this paper, we continue to investigate some properties of the family Γ of finite-dimensional simple modular Lie superalgebras which were constructed by X. N. Xu, Y. Z. Zhang, L. Y. Chen (2010). For each algebra in the family, a filtration is defined and proved to be invariant under the automorphism group. Then an intrinsic property is proved by the invariance of the filtration; that is, the integer parameters in the definition of Lie superalgebras Γ are intrinsic. Thereby, we classify these Lie superalgebras in the sense of isomorphism. Finally, we study the associative forms and Killing forms of these Lie superalgebras and determine which superalgebras in the family are restrictable. 相似文献
12.
《代数通讯》2013,41(6):2149-2175
Abstract In this paper we show that a Lie superalgebra L graded by a 3-graded irreducible root system has Gelfand–Kirillov dimension equal to the Gelfand–Kirillov dimension of its coordinate superalgebra A, and that L is locally finite if and only A is so. Since these Lie superalgebras are coverings of Tits–Kantor–Koecher superalgebras of Jordan superpairs covered by a connected grid, we obtain our theorem by combining two other results. Firstly, we study the transfer of the Gelfand–Kirillov dimension and of local finiteness between these Lie superalgebras and their associated Jordan superpairs, and secondly, we prove the analogous result for Jordan superpairs: the Gelfand–Kirillov dimension of a Jordan superpair V covered by a connected grid coincides with the Gelfand– Kirillov dimension of its coordinate superalgebra A, and V is locally finite if and only if A is so. 相似文献
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The algebraic trace form (as defined by O. Loos) of an element(x, y) of a (complex) Banach Jordan pair V, where x or y isin the socle, is equal to the sum of the products of all spectralvalues and their multiplicity. The trace form is calculatedfor two examples, the Banach Jordan pair of bounded linear operatorsbetween two Banach spaces, and the Banach Jordan pair of a quadraticform. Using analytic multifunctions, it is also shown that thecomplement of the socle of a Banach Jordan pair V is eitherdense or empty. In the last case, V has finite capacity. 1991Mathematics Subject Classification 17C65, 46H70. 相似文献
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The Lie superalgebras in the extended Freudenthal Magic Square in characteristic 3 are shown to be related to some known simple
Lie superalgebras, specific to this characteristic, constructed in terms of orthogonal and symplectic triple systems, which
are defined in terms of central simple degree three Jordan algebras.
I. Cunha was supported by CMUC, Department of Mathematics, University of Coimbra.
A. Elduque was supported by the Spanish Ministerio de Educación y Ciencia and FEDER (MTM 2004-081159-C04-02) and by the Diputación
General de Aragón (Grupo de Investigación de álgebra). 相似文献
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Abstract In this paper, the super t~-operators of Jordan superalgebras are introduced and the solutions of super Jordan Yang-Baxter equation are discussed by super б-operators. Then pre-Jordan superalgebras are studied as the algebraic structure behind the super б-operators. Moreover, the relations among Jordan superalgebras, pre-Jordan superalgebras, and dendriform superalgebras are established. Keywords Super б-operator, dendriform superalgebra, pre-Jordan superalgebra 相似文献
18.
V. N. Zhelyabin 《Siberian Mathematical Journal》2018,59(6):1051-1062
Studying the unital simple Jordan superalgebras with associative even part, we describe the unital simple Jordan superalgebras such that every pair of even elements induces the zero derivation and every pair of two odd elements induces the zero derivation of the even part. We show that such a superalgebra is either a superalgebra of nondegenerate bilinear form over a field or a four-dimensional simple Jordan superalgebra. 相似文献
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We describe Novikov-Poisson algebras in which a Novikov algebra is not simple while its corresponding associative commutative
derivation algebra is differentially simple. In particular, it is proved that a Novikov algebra is simple over a field of
characteristic not 2 iff its associative commutative derivation algebra is differentially simple. The relationship is established
between Novikov-Poisson algebras and Jordan superalgebras.
Supported by RFBR (grant No. 05-01-00230), by SB RAS (Integration project No. 1.9), and by the Council for Grants (under RF
President) and State Aid of Leading Scientific Schools (project NSh-344.2008.1).
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Translated from Algebra i Logika, Vol. 47, No. 2, pp. 186–202, March–April, 2008. 相似文献
20.
V. N. Zhelyabin 《Siberian Mathematical Journal》2016,57(6):987-1001
Under study are the simple infinite-dimensional abelian Jordan superalgebras not isomorphic to the superalgebra of a bilinear form. We prove that the even part of such superalgebra is a differentially simple associative commutative algebra, and the odd part is a finitely generated projective module of rank 1. We describe unital simple Jordan superalgebras with associative nil-semisimple even part possessing two even elements which induce a nonzero derivation. 相似文献