共查询到20条相似文献,搜索用时 15 毫秒
1.
Dessislava H. Kochloukova 《代数通讯》2013,41(3):785-796
We define and study the property finite presentability in the category of Hopf algebras that are smash product of universal enveloping algebra of a Lie algebra by a group algebra. We show that for such Hopf algebras finite presentability is equivalent with finite presentability as an associative k-algebra. 相似文献
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V. M. Petrogradsky 《代数通讯》2013,41(3):918-928
We study Lie nilpotent varieties of associative algebras. We explicitly compute the codimension growth for the variety of strong Lie nilpotent associative algebras. The codimension growth is polynomial and found in terms of Stirling numbers of the first kind. To achieve the result we take the free Lie algebra of countable rank L(X), consider its filtration by the lower central series and shift it. Next we apply generating functions of special type to the induced filtration of the universal enveloping algebra U(L(X)) = A(X). 相似文献
4.
Francesco Catino Salvatore Siciliano Ernesto Spinelli 《Algebras and Representation Theory》2010,13(6):653-660
Let L be a non-abelian restricted Lie algebra over a field of characteristic p > 0 and let u(L) denote its restricted enveloping algebra. In Siciliano (Publ Math (Debr) 68:503–513, 2006) it was proved that if u(L) is Lie solvable then the Lie derived length of u(L) is at least ⌈log2(p + 1)⌉. In the present paper we characterize the restricted enveloping algebras whose Lie derived length coincides with this
lower bound. 相似文献
5.
Lie antialgebras is a class of supercommutative algebras recently appeared in symplectic geometry. We define the notion of
enveloping algebra of a Lie antialgebra and study its properties. We show that every Lie antialgebra is canonically related
to a Lie superalgebra and prove that its enveloping algebra is a quotient of the enveloping algebra of the corresponding Lie
superalgebra. 相似文献
6.
WANG Gui-dong 《数学季刊》2005,20(4):423-429
In this paper, we mainly concerned about the nilpotence of Lie triple algebras. We give the definition of nilpotence of the Lie triple algebra and obtained that if Lie triple algebra is nilpotent, then its standard enveloping Lie algebra is nilpotent. 相似文献
7.
We use the fusion construction in twisted quantum affine algebras to obtain a unified method to deform the wedge product for classical Lie algebras. As a by-product we uniformly realize all non-spin fundamental modules for quantized enveloping algebras of classical types, and show that they admit natural crystal bases as modules for the (derived) twisted quantum affine algebra. These crystal bases are parametrized in terms of the q-wedge products. 相似文献
8.
José M. Pérez-Izquierdo 《Advances in Mathematics》2007,208(2):834-876
Sabinin algebras are a broad generalization of Lie algebras that include Lie, Malcev and Bol algebras as very particular examples. We present a construction of a universal enveloping algebra for Sabinin algebras, and the corresponding Poincaré-Birkhoff-Witt Theorem. A nonassociative counterpart of Hopf algebras is also introduced and a version of the Milnor-Moore Theorem is proved. Loop algebras and universal enveloping algebras of Sabinin algebras are natural examples of these nonassociative Hopf algebras. Identities of loops move to identities of nonassociative Hopf algebras by a linearizing process. In this way, nonassociative algebras and Hopf algebras interlace smoothly. 相似文献
9.
We give a presentation of the Schur algebras S
Q
(2,d) by generators and relations, in fact a presentation which is compatible with Serre's presentation of the universal enveloping algebra of a simple Lie algebra. In the process we find a new basis for S
Q
(2,d), a truncated form of the usual PBW basis. We also locate the integral Schur algebra within the presented algebra as the analogue of Kostant's Z-form, and show that it has an integral basis which is a truncated version of Kostant's basis. 相似文献
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Finite vs affine W-algebras 总被引:1,自引:0,他引:1
In Section 1 we review various equivalent definitions of a vertex algebra V. The main novelty here is the definition in terms of an indefinite integral of the λ-bracket. In Section 2 we construct,
in the most general framework, the Zhu algebra ZhuΓV, an associative algebra which “controls” Γ-twisted representations of the vertex algebra V with a given Hamiltonian operator H. An important special case of this construction is the H-twisted Zhu algebra ZhuH V. In Section 3 we review the theory of non-linear Lie conformal algebras (respectively non-linear Lie algebras). Their universal
enveloping vertex algebras (resp. universal enveloping algebras) form an important class of freely generated vertex algebras
(resp. PBW generated associative algebras). We also introduce the H-twisted Zhu non-linear Lie algebra ZhuH R of a non-linear Lie conformal algebra R and we show that its universal enveloping algebra is isomorphic to the H-twisted Zhu algebra of the universal enveloping vertex algebra of R. After a discussion of the necessary cohomological material in Section 4, we review in Section 5 the construction and basic
properties of affine and finite W-algebras, obtained by the method of quantum Hamiltonian reduction. Those are some of the
most intensively studied examples of freely generated vertex algebras and PBW generated associative algebras. Applying the
machinery developed in Sections 3 and 4, we then show that the H-twisted Zhu algebra of an affine W-algebra is isomorphic to the finite W-algebra, attached to the same data. In Section 6
we define the Zhu algebra of a Poisson vertex algebra, and we discuss quasiclassical limits. In the Appendix, the equivalence
of three definitions of a finite W-algebra is established.
“I am an old man, and I know that a definition cannot be so complicated.” I.M. Gelfand (after a talk on vertex algebras in
his Rutgers seminar) 相似文献
12.
In this article, we give a sufficient condition for a Lie color algebra to be complete. The color derivation algebra Der(?) and the holomorph L of finite dimensional Heisenberg Lie color algebra ? graded by a torsion-free abelian group over an algebraically closed field of characteristic zero are determined. We prove that Der(?) and Der(L) are simple complete Lie color algebras, but L is not a complete Lie color algebra. 相似文献
13.
Ivan Marin 《代数通讯》2013,41(7):2572-2584
We consider the natural Lie algebra structure on the (associative) group algebra of a finite group G, and show that the Lie subalgebras associated to natural involutive antiautomorphisms of this group algebra are reductive ones. We give a decomposition in simple factors of these Lie algebras, in terms of the ordinary representations of G. 相似文献
14.
Robert Laugwitz 《Algebras and Representation Theory》2016,19(3):547-578
In this paper, we present an approach to the definition of multiparameter quantum groups by studying Hopf algebras with triangular decomposition. Classifying all of these Hopf algebras which are of what we call weakly separable type over a group, we obtain a class of pointed Hopf algebras which can be viewed as natural generalizations of multiparameter deformations of universal enveloping algebras of Lie algebras. These Hopf algebras are instances of a new version of braided Drinfeld doubles, which we call asymmetric braided Drinfeld doubles. This is a generalization of an earlier result by Benkart and Witherspoon (Algebr. Represent. Theory 7(3) ? BC) who showed that two-parameter quantum groups are Drinfeld doubles. It is possible to recover a Lie algebra from these doubles in the case where the group is free abelian and the parameters are generic. The Lie algebras arising are generated by Lie subalgebras isomorphic to \(\mathfrak {sl}_{2}\). 相似文献
15.
Comtrans algebras, as analogues of Lie algebras, provide tangent bundle structure corresponding to web geometry in a manifold. In this article, restricted comtrans algebras over rings of small odd prime characteristic are introduced, as analogues of restricted Lie algebras. It is shown that their representations are equivalent to modules over a restricted universal enveloping algebra. 相似文献
16.
Classical r-Matrices and Novikov Algebras 总被引:1,自引:0,他引:1
Dietrich Burde 《Geometriae Dedicata》2006,122(1):145-157
We study the existence problem for Novikov algebra structures on finite-dimensional Lie algebras. We show that a Lie algebra
admitting a Novikov algebra is necessarily solvable. Conversely we present a 2-step solvable Lie algebra without any Novikov
structure. We use extensions and classical r-matrices to construct Novikov structures on certain classes of solvable Lie algebras. 相似文献
17.
Chaowen Zhang 《Algebras and Representation Theory》2013,16(2):445-470
Let $ \mathfrak{g} $ be a restricted Lie color algebra. We define the p-character χ and study the χ-reduced enveloping algebras. We define the reductive Lie color algebras and FP triples, and study the representations associated with FP triples. As an application, we prove an analogue of the Kac-Weisfeiler theorem and determine the simplicity of the baby Verma module for the general linear Lie color algebra $ \mathfrak{g}= {\rm{gl}} (V)$ . 相似文献
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20.
J. Mostovoy 《代数通讯》2013,41(1):185-194
In this note we point out that the definition of the universal enveloping dialgebra for a Leibniz algebra is consistent with the interpretation of a Leibniz algebra as a generalization not of a Lie algebra, but of the adjoint representation of a Lie algebra. From this point of view, the formal integration problem of Leibniz algebras is, essentially, trivial. 相似文献