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991.
Plamen Koshlukov 《代数通讯》2013,41(7):3095-3113
Let L be a Lie algebra, nilpotent of class 2, over an infinite field K, and suppose that the centre C of L is one dimensional; such Lie algebras are called Heisenberg algebras. Let ρ:L→hom KV be a finite dimensional representation of the Heisenberg algebra L such that ρ(C) contains non-singular linear transformations of V, and denote l(ρ) the ideal of identities for the representation ρ. We prove that the ideals of identities of representations containing I(ρ) and generated by multilinear polynomials satisfy the ACC. Let sl 2(L) be the Lie algebra of the traceless 2×2 matrices over K, and suppose the characteristic of K equals 2. As a corollary we obtain that the ideals of identities of representations of Lie algebras containing that of the regular representation of sl 2(K) and generated by multilinear polynomials, are finitely based. In addition we show that one cannot simply dispense with the condition of multilinearity. Namely, we show that the ACC is violated for the ideals of representations of Lie algebras (over an infinite field of characteristic 2) that contain the identities of the regular representation of sl 2(K). 相似文献
992.
Compact Exceptional Simple Kantor Triple Systems Defined on Tensor Products of Composition Algebras∗
Daniel Mondoc 《代数通讯》2013,41(11):3699-3712
In this article we give the classification of compact exceptional simple Kantor triple systems defined on tensor products of composition algebras A = 1? 2 such that their Kantor algebras ?(φ, A) are real forms of exceptional simple Lie algebras. 相似文献
993.
994.
Let KGbe the group algebra of a p1 -group Gover a field Kof characteristic p > 0, and let U(KG)be its group of units. If KGcontains a nontrivial bicyclic unit and if Kis not algebraic over its prime field, then we prove that the free product Zp? Zp? Zpcan be embedded in U(KG). 相似文献
995.
Let G be an abelian group and let R be a commutative ring with identity. Denote by R t G a commutative twisted group algebra (a commutative twisted group ring) of G over R, by ?(R) and ?(R t G) the nil radicals of R and R t G, respectively, by G p the p-component of G and by G 0 the torsion subgroup of G. We prove that:
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If R is a ring of prime characteristic p, the multiplicative group R* of R is p-divisible and ?(R) = 0, then there exists a twisted group algebra R t 1 (G/G p ) such that R t G/?(R t G) ? R t 1 (G/G p ) as R-algebras;
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If R is a ring of prime characterisitic p and R* is p-divisible, then ?(R t G) = 0 if and only if ?(R) = 0 and G p = 1; and
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If B(R) = 0, the orders of the elements of G 0 are not zero divisors in R, H is any group and the commutative twisted group algebra R t G is isomorphic as R-algebra to some twisted group algebra R t 1 H, then R t G 0 ? R t 1 H 0 as R-algebras.
996.
Mohammad Hassanzadeh 《代数通讯》2013,41(12):5287-5298
In this note, the categories of coefficients for Hopf cyclic cohomology of comodule algebras and comodule coalgebras are extended. We show that these new categories have two proper different subcategories where the smallest one is the known category of stable anti Yetter–Drinfeld modules. We prove that components of Hopf cyclic cohomology such as cup products work well with these new coefficients. 相似文献
997.
Fernando Fantino 《代数通讯》2013,41(10):4426-4434
998.
Andre Fonseca 《代数通讯》2013,41(9):3686-3694
999.
1000.
Among the involutions of a Clifford algebra, those induced by the involutions of the orthogonal group are the most natural ones. In this work, several basic properties of these involutions, such as the relations between their invariants, their occurrences, and their decompositions, are investigated. 相似文献