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V. N. Zhelyabin 《Algebra and Logic》1995,34(1):25-34
In the article we show that a Jordan superalgebra over a ring with unity, containing an element 1/3, is solvable whenever its even part is solvable.Translated fromAlgebra i Logika, Vol. 34, No. 1, pp. 44–60, January–February, 1995. 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
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An algebra obtained by the external adjoining a unit to a nilalgebra is said to be unitary. It is proved that every simple finite-dimensional right alternative superalgebra with unitary even part over a field of characteristic 0 is associative. 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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The maximal subalgebras of the finite-dimensional simple special Jordan superalgebras over an algebraically closed field of characteristic 0 are studied. This is a continuation of a previous paper by the same authors about maximal subalgebras of simple associative superalgebras, which is instrumental here. 相似文献
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V. N. Zhelyabin 《Siberian Advances in Mathematics》2010,20(3):223-230
In [14], a new example is constructed of a unital simple special Jordan superalgebra J over the field of reals. It turns out that J is a subsuperalgebra of a Jordan superalgebra of vector type but it cannot be isomorphic to a superalgebra of such a type. Moreover, the superalgebra of fractions of J is isomorphic to a Jordan superalgebra of vector type. In the present article, we find a similar example of a Jordan superalgebra. It is constructed over a field of characteristic 0 in which the equation t 2 + 1 = 0 has no solutions. 相似文献
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代数A称为不可分解的,如果A不能分解成理想的直和.证明了满足C(L_o)=C(L)={0}的Jordan李超代数L一些重要性质. 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
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N. B. Kaygorodov 《Algebra and Logic》2007,46(5):318-329
We describe non-trivial δ-derivations of semisimple finite-dimensional Jordan algebras over an algebraically closed field
of characteristic not 2, and of simple finite-dimensional Jordan superalgebras over an algebraically closed field of characteristic
0. For these classes of algebras and superalgebras, non-zero δ-derivations are shown to be missing for δ ≠ 0, 1/2, 1, and
we give a complete account of 1/2-derivations.
Supported by RFBR grant No. 05-01-00230 and by RF Ministry of Education and Science grant No. 11617.
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Translated from Algebra i Logika, Vol. 46, No. 5, pp. 585–605, September–October, 2007. 相似文献
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LetR be a semiprime algebra over a fieldK acted on by a finite-dimensional Lie superalgebraL. The purpose of this paper is to prove a series of going-up results showing how the structure of the subalgebra of invariantsR Lis related to that ofR. Combining several of our main results we have: Theorem: Let R be a semiprime K-algebra acted on by a finite-dimensional nilpotent Lie superalgebra L such that if characteristic K=p then L is restricted and if characteristic, K=0 then L acts on R as algebraic derivations and algebraic superderivations.
- If RL is right Noetherian, then R is a Noetherian right RL-module. In particular, R is right Noetherian and is a finitely generated right RL-module.
- If RL is right Artinian, then R is an Artinian right RL-module. In particular, R is right Artinian and is a finitely generated right RL-module.
- If RL is finite-dimensional over K then R is also finite-dimensional over K.
- If RL has finite Goldie dimension as a right RL-module, then R has finite Goldie dimension as a right R-module.
- If RL has Krull dimension α as a right RL-module, then R has Krull dimension α as a right RL-module. Thus R has Krull dimension at most α as a right R-module.
- If R is prime and RL is central, then R satisfies a polynomial identity.
- If L is a Lie algebra and RL is central, then R satisfies a polynomial identity.
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We investigate the Jordan structure of a prime associative superalgebra and the Jordan structure of the symmetric elements of a *-prime associative superalgebra with superinvolution. 相似文献
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V. N. Zhelyabin 《Siberian Mathematical Journal》2013,54(1):33-39
We construct some examples of prime Jordan superalgebras of vector type whose odd part is a finitely generated projective module of rank 1 with arbitrarily many generators. These provide some examples of prime Jordan superalgebras of Cheng-Kac type. 相似文献
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