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1.
2.
A. M. Kuz’min 《Journal of Mathematical Sciences》2008,149(2):1098-1106
A sufficient condition is proved for the Specht property of varieties of right alternative metabelian algebras over a field
of characteristic distinct from 2. As a consequence, the Specht property of some varieties generated by right alternative
metabelian algebras A satisfying a commutator identity is stated. In particular, it is proved that if A
(−) is a binary Lie algebra, then var(A) is Spechtian.
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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 2, pp. 89–100, 2006. 相似文献
3.
D. M. Riley proved in [3] that, if A and
B are either Lie nilpotent or Lie metabelian algebras, then their tensor product A ⊗ B is Lie soluble and obtained bounds on the Lie derived length of A ⊗ B. The aim of the present note is to improve Riley’s bounds; moreover we consider also the cases in which A and B are either strongly Lie soluble or strongly Lie nilpotent algebras.
Received: 5 April 2006
The first two authors partially supported by MIUR-Italy via PRIN “Group theory and applications”. 相似文献
4.
A Lie module algebra for a Lie algebra L is an algebra and L-module A such that L acts on A by derivations. The depth Lie algebra of a Lie algebra L with Lie module algebra A acts on a corresponding depth Lie module algebra . This determines a depth functor from the category of Lie module algebra pairs to itself. Remarkably, this functor preserves central simplicity. It follows
that the Lie algebras corresponding to faithful central simple Lie module algebra pairs (A,L) with A commutative are simple. Upon iteration at such (A,L), the Lie algebras are simple for all i ∈ ω. In particular, the (i ∈ ω) corresponding to central simple Jordan Lie algops (A,L) are simple Lie algebras.
Presented by Don Passman. 相似文献
5.
Simple algebras of Weyl type 总被引:9,自引:0,他引:9
Over a fieldF of arbitrary characteristic, we define the associative and the Lie algebras of Weyl type on the same vector spaceA[D] =A⊗F[D] from any pair of a commutative associative algebra,A with an identity element and the polynomial algebraF[D] of a commutative derivation subalgebraD ofA We prove thatA[D], as a Lie algebra (modulo its center) or as an associative algebra, is simple if and only ifA isD-simple andA[D] acts faithfully onA. Thus we obtain a lot of simple algebras.
Su, Y., Zhao, K., Second cohornology group of generalized Witt type Lie algebras and certain representations, submitted to
publication 相似文献
6.
We characterize the restricted Lie algebras L whose restricted universal enveloping algebra u(L) is Lie metabelian. Moreover, we show that the last condition is equivalent to u(L) being strongly Lie metabelian.Received: 1 October 2004 相似文献
7.
In one of our recent papers, the associative and the Lie algebras of Weyl typeA[D]=A⊗F[D] were defined and studied, whereA is a commutative associative algebra with an identity element over a field F of any characteristic, and F[D] is the polynomial algebra of a commutative derivation subalgebraD ofA. In the present paper, a class of the above associative and Lie algebrasA[D] with F being a field of characteristic 0,D consisting of locally finite but not locally nilpotent derivations ofA, are studied. The isomorphism classes and automorphism groups of these associative and Lie algebras are determined 相似文献
8.
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
9.
In this paper the main result is the rigidity of varietally free Lie algebras within the varieties where they are free. In fact, these algebras are usually free in some larger varieties, such as various types of the commutator varieties, and this is demonstrated in this paper as well. A related paper is [2] where, among some other results, we claimed the rigidity of free metabelian algebras within the respective variety of Lie algebras. 相似文献
10.
A class of graded simple associative algebras are constructed, and from them, simple Lie color algebras are obtained. The
structure of these simple Lie color algebras is explicitly described. More precisely, for an (ε, Γ)-color-commutative associative algebraA with an identity element over a fieldF of characteristic not 2, and for a color-commutative subalgebraD of color-derivations ofA, denote byA[D] the associative subalgebra of End (A) generated byA (regarded as operators onA via left multiplication) andD. It is easily proved that, as an associative algebra,A[D] is Γ-graded simple if and only ifA is Γ-gradedD-simple. SupposeA is Γ-gradedD-simple. Then, (a)A[D] is a free leftA-module; (b) as a Lie color algebra, the subquotient [A[D],A[D]]/Z(A[D])∩[A[D],A[D]] is simple (except one minor case), whereZ(A[D]) is the color center ofA[D].
This work was supported by NSF of China, National Educational Department of China, Jiangsu Educational Committee, and Hundred
Talents Program of Chinese Academy of Sciences.
These authors were partially supported by Academy of Mathematics and System Sciences during their visit to this academy. 相似文献
11.
Among thin graded Lie algebras, which are particular instances of Lie algebras of finite width, there are many interesting objects, such as the graded Lie algebra associated to the Nottingham group. Among the factors of a thin algebra with respect to the terms of the lower central series, there is a greatest factor which is of maximal class. In thin Lie algebras associated to groups, this factor is metabelian. In this paper we show that the same holds in general, provided the characteristic of the underlying field is odd. In another paper by the second author it is shown that this is not the case for characteristic two. 相似文献
12.
It is proved that, for any metabelian Mal'tsev algebra M over a field of characteristic 2,3, there is an alternative algebra A such that the algebra M can be embedded in the commutator algebra A(-). Moreover, the enveloping alternative algebra A can be found in the variety of algebras with the identity [x,y][z,t] = 0. The proof of this result is based on the construction of additive bases of the free metabelian Mal'tsev algebra and the free alternative algebra with the identity [x,y][z,t] = 0. 相似文献
13.
The classification of extended affine Lie algebras of type A_1 depends on the Tits-Kantor- Koecher (TKK) algebras constructed from semilattices of Euclidean spaces.One can define a unitary Jordan algebra J(S) from a semilattice S of R~v (v≥1),and then construct an extended affine Lie algebra of type A_1 from the TKK algebra T(J(S)) which is obtained from the Jordan algebra J(S) by the so-called Tits-Kantor-Koecher construction.In R~2 there are only two non-similar semilattices S and S′,where S is a lattice and S′is a non-lattice semilattice.In this paper we study the Z~2-graded automorphisms of the TKK algebra T(J(S)). 相似文献
14.
D. V. Millionshchikov 《Proceedings of the Steklov Institute of Mathematics》2008,263(1):99-111
We compute explicitly the adjoint cohomology of two ℕ-graded Lie algebras of maximal class (infinite-dimensional filiform
Lie algebras) m0 and m2. It is known that up to an isomorphism there are only three ℕ-graded Lie algebras of maximal class. The third algebra from
this list is the “positive” part L
1 of the Witt (or Virasoro) algebra, and its adjoint cohomology was computed earlier by Feigin and Fuchs.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 263, pp. 106–119. 相似文献
15.
We characterise the modulesB of homological typeFP
m
over a finitely generated Lie algebraL such thatL is a split extension of an abelian idealA and an abelian subalgebraQ andA acts trivially onB. The characterisation is in terms of the invariant Δ introduced by R. Bryant and J. Groves and is a Lie algebra version of
the generalisation [K 4, conjecture 1] of the still openFP
m
-Conjecture for metabelian groups [Bi-G, Conjecture p. 367]. The casem=1 of our main result is treated separately, as there the characterisation is proved without restrictions on the type of the
extension. 相似文献
16.
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
17.
A. I. Generalov 《Journal of Mathematical Sciences》2006,134(6):2489-2510
The present paper continues a series of papers by the author (some of them are written in collaboration) in which the Yoneda
algebra is calculated for several families of algebras of dihedral and semidihedral type (in K. Erdmann’s classification).
In the present paper, the Yoneda algebra is described (in terms of quivers with relations) for algebras of semidihedral type,
namely, of the families SD(2A)1, SD(2A)2, and SD(3A)2. Bibliography: 13 titles.
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Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 319, 2004, pp. 71–116. 相似文献
18.
Ming FANG 《数学学报(英文版)》2008,24(2):311-318
Let A be a QF-3 standardly stratified algebra and f be a Schur functor corresponding to some projective-injective faithful A-module, denoted by Ae. The main result of this paper is to prove that, if the dominant dimension of A is sufficiently large, then ] induces a full embedding from £(△) to eAe-mod which preserves Ext-groups up to certain degrees, where £(△) denotes the full subcategory of A-mod whose objects are filtered by standard A-modules. We check this criterion on some typical examples, quantized Schur algebras Sq(n,r) with n≥r and finite-dimensional algebras associated with the Bernstein-Gelfand-Gelfand category O of semisimple complex Lie algebras. 相似文献
19.
20.
We study the Lie structure of graded associative algebras. Essentially, we analyze the relation between Lie and associative graded ideals, and between Lie and associative graded derivations. Gathering together results on both directions, we compute maximal graded algebras of quotients of graded Lie algebras that arise from associative algebras. We also show that the Lie algebra Der gr (A) of graded derivations of a graded semiprime associative algebra is strongly non-degenerate (modulo a certain ideal containing the center of Der gr (A)). 相似文献