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本文引入模代数的一种新对偶,它推广了代数的有限对偶概念,并证明:通过这种新对偶,模代数的对偶为余模余代数,从而形成Smash余积,而且证明了Smash积的对偶是Smash余积,即有(A#H)~0 _HA~0×H~0余代数同构,最后证明量子模范畴中的Hopf代数通过这种新对偶是自对偶的。  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
3.
In this paper, we give some basic properties of the generalized derivation algebra GDer(L) of a Lie color algebra L. In particular, we prove that GDer(L) = QDer(L) + QC(L), the sum of the quasiderivation algebra and the quasicentroid. We also prove that QDer(L) can be embedded as derivations in a larger Lie color algebra.  相似文献
4.
A new family of finite-dimensional simple modular Lie superalgebra ? is constructed based on results of Y. Z. Zhang and Q. C. Zhang [J. Algebra, 2009, 321: 3601–3619]. The simplicity and generators of ? are discussed and the derivation superalgebra of ? is characterized. Furthermore, the invariance of the nonnatural filtration of ? is determined by the method of minimal dimension of image spaces.  相似文献
5.
People studied the properties and structures of restricted Lie algebras all whose elements are semisimple. It is the main objective of this paper to continue the investigation in order to obtain deeper structure theorems. We obtain some sufficient conditions for the commutativity of restricted Lie algebras, generalize some results of R. Farnsteiner and characterize some properties of a finite-dimensional semisimple restricted Lie algebra all whose elements are semisimple. Moreover, we show that a centralsimple restricted Lie algebra all whose elements are semisimple over a field of characteristic p > 7 is a form of a classical Lie algebra.  相似文献
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In this paper, we construct two kinds of Novikov algebras, characterize some properties of them and give their realizations by triangle functions, respectively.  相似文献
7.
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Hom-Lie conformal algebras. In this paper, we develop cohomology theory of Hom-Lie conformal algebras and discuss some applications to the study of deformations of regular Hom-Lie conformal algebras. Also, we introduce α~k-derivations of multiplicative Hom-Lie conformal algebras and study their properties.  相似文献
8.
In this paper, we investigate the Leibniz triple system T and its universal Leibniz envelope U(T). The involutive automorphism of U(T) determining T is introduced, which gives a characterization of the \(\mathbb {Z}_{2}\)-grading of U(T). We show that the category of Leibniz triple systems is equivalent to a full subcategory of the category of \(\mathbb {Z}_{2}\)-graded Leibniz algebras. We give the relationship between the solvable radical R(T) of T and R a d(U(T)), the solvable radical of U(T). Further, Levi’s theorem for Leibniz triple systems is obtained. Moreover, the relationship between the nilpotent radical of T and that of U(T) is studied. Finally, we introduce the notion of representations of a Leibniz triple system, which can be described by using involutive representations of its universal Leibniz envelope.  相似文献
9.
Let F be the underlying base field of characteristic p > 3 and denote by M the even part of the finite-dimensional simple modular Lie superalgebra M. In this paper, the generator sets of the Lie algebra M which will be heavily used to consider the derivation algebra Der(M) are given. Furthermore, the derivation algebra of M is determined by reducing derivations and a torus of M, i.e.,As a result, the derivation algebra of the even part of M does not equal the even part of the derivation superalgebra of M.  相似文献
10.
The main purpose of the present paper is to give some properties of the Jacobson radical,the Frattini subsystem and c-ideals of a Lie triple system.Some further results concerning the Frattini subsystems of nilpotent and solvable Lie triple systems are obtained.Moreover,we develop initially c-ideals for a Lie triple system and make use of them to give some characterizations of a solvable Lie triple system.  相似文献
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