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1.
Generalized table algebras were introduced in Arad, Fisman and Muzychuk (Israel J. Math.
114 (1999), 29–60) as an axiomatic closure of some algebraic properties of the Bose-Mesner algebras of association schemes. In this note we show that if all non-trivial degrees of a generalized integral table algebra are even, then the number of real basic elements of the algebra is bounded from below (Theorem 2.2). As a consequence we obtain some interesting facts about association schemes the non-trivial valencies of which are even. For example, we proved that if all non-identical relations of an association scheme have the same valency which is even, then the scheme is symmetric. 相似文献
2.
Adriana Nenciu 《Algebras and Representation Theory》2004,7(2):159-172
We study the quasitriangular structures for a family of pointed Hopf algebras which is big enough to include Taft's Hopf algebras H
n
2, Radford's Hopf algebras H
N,n,q, and E(n). We give necessary and sufficient conditions for the Hopf algebras in our family to be quasitriangular. For the case when they are, we determine completely all the quasitriangular structures. Also, we determine the ribbon elements of the quasitriangular Hopf algebras and the quasi-ribbon elements of their Drinfel'd double. 相似文献
3.
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
4.
Surjit Singh Khurana 《Czechoslovak Mathematical Journal》2001,51(2):433-437
Let X be a completely regular Hausdorff space, Cb(X) the space of all scalar-valued bounded continuous functions on X with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally m-convex. 相似文献
5.
We define an equivariant K
0-theory for Yetter–Drinfeld algebras over a Hopf algebra with an invertible antipode. We then show that this definition can be generalized to all Hopf-module algebras. We show that there exists a pairing, generalizing Connes pairing, between this theory and a suitably defined Hopf algebra equivariant cyclic cohomology theory. 相似文献
6.
We introduce the definition of pseudoorthoalgebras and discuss some relationships between orthomodular lattices and pseudoorthoalgebras.
Then we study the conditions that a pseudoeffect algebra is isomorphic to an “internal direct product” of ideals generated
by orthogonal principal elements. At last, we give some characterizations of central elements in pseudoeffect algebras. 相似文献
7.
8.
Michihisa Wakui 《Algebras and Representation Theory》2004,7(5):491-515
We determine various additional structures on all nonsemisimple Hopf algebras of dimension 8 over an algebraically closed
field k of characteristic 0, including their representation rings and quasitriangular structures. As a consequence, it is shown that
for two such Hopf algebras, the tensor categories of their representations are monoidally equivalent if and only if the representation
rings of them are isomorphic as rings.
An erratum to this article is available at . 相似文献
9.
Askar Dzhumadil’daev 《代数通讯》2018,46(1):129-142
We prove that assosymmetric algebras under the Jordan product are Lie triple algebras. A Lie triple algebra is called special if it is isomorphic to a subalgebra of the plus-algebra of some assosymmetric algebra. We establish that the Glennie identity of degree 8 is valid for special Lie triple algebras, but not for all Lie triple algebras. 相似文献
10.
In an article by Michaelis, a class of infinite-dimensional Lie bialgebras containing the Virasoro algebra was presented. This type of Lie bialgebras was classified by Ng and Taft. In a recent article by Song and Su, Lie bialgebra structures on graded Lie algebras of generalized Witt type with finite dimensional homogeneous components were considered. In this article we consider Lie bialgebra structures on the graded Lie algebras of generalized Witt type with infinite dimensional homogeneous components. By proving that the first cohomology group H1(𝒲, 𝒲 ? 𝒲) is trivial for any graded Lie algebras 𝒲 of generalized Witt type with infinite dimensional homogeneous components, we obtain that all such Lie bialgebras are triangular coboundary. 相似文献
11.
We mainly study the super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras. In particular, we prove that all super-biderivations of not-finitely graded Lie superalgebras related to generalized super-Virasoro algebras are inner. 相似文献
12.
《代数通讯》2013,41(11):5467-5479
Abstract In this paper, we generalize the concept of purely imaginary roots of Kac–Moody algebras to generalized Kac–Moody algebras. Also we give a complete classification of those generalized Kac–Moody algebras with the purely imaginary property. We also define a new class of indefinite non-hyperbolic generalized Kac–Moody algebras called extended hyperbolic generalized Kac–Moody algebras and find that it does not always possess the purely imaginary property whereas the extended hyperbolic Kac–Moody algebras possess the purely imaginary property. 相似文献
13.
In a previous paper, the first-named author introduced generalized structurable algebras, while the second-named author introduced the isotopies of Lie algebras. In this paper, we combine the two analyses, submit the notion of isogeneralized structural algebras, and show that they include Lie algebras, all their axiom-preserving generalizations of graded, supersymmetric or isotopic type, as well as numerous other algebras. 相似文献
14.
This is a contribution to the classification of finite-dimensional pointed Hopf algebras. We are concerned with the case when the group of group-like elements is Abelian of exponent 2. We attach to such a pointed Hopf algebra a generalized simply-laced Cartan matrix; we conjecture that the Hopf algebra is finite-dimensional if and only if the Cartan matrix is of finite type. We prove the conjecture for the types An and An(1). We obtain the classification of all possible Hopf algebras with Cartan matrix An. We use the lifting method developed by Hans-Jürgen Schneider and the first-named author.
Presented by S. MontgomeryMathematics Subject Classifications (2000) Primary: 17B37; secondary: 16W30.This work was partially supported by CONICET, Agencia Córdoba Ciencia – CONICOR, FOMEC and Secyt (UNC). 相似文献
15.
ON THE COHOMOLOGY OF GENERALIZED RESTRICTED LIE ALGEBRAS 总被引:2,自引:0,他引:2
Shu Bin 《数学年刊B辑(英文版)》1998,19(4):421-432
0.IntroductionThispaperisaimedatdevelopingthecohomologytheoryofmodularLiealgebrasandthendeterminingthefirstcohomologygroupsofCartantypeLiealgebras.AsgeneralizationoftheconceptofrestrictedLiealgebras,ageneralizedrestrictedLiealgebra(GRLiealgebra)wasintroducedin[21],whichisassociatedwithabasisandamappingofthebasisintotheLiealgebrasatisfyingthegeneralized-restrictednessconditions.Generalizedrestrictedrepresentations(GRrepresentations)werethenintroduced,whichcanbereducedtotherepresentationsofa… 相似文献
16.
Ualbai Umirbaev 《代数通讯》2017,45(7):2809-2820
A structure of a left-symmetric algebra on the set of all derivations of a free algebra is introduced such that its commutator algebra becomes the usual Lie algebra of derivations. Left and right nilpotent elements of left-symmetric algebras of derivations are studied. Simple left-symmetric algebras of derivations and Novikov algebras of derivations are described. It is also proved that the positive part of the left-symmetric algebra of derivations of a free nonassociative symmetric m-ary algebra in one free variable is generated by one derivation and some right nilpotent derivations are described. 相似文献
17.
Nicolas Guay 《Advances in Mathematics》2007,211(2):436-484
We study the structure of Yangians of affine type and deformed double current algebras, which are deformations of the enveloping algebras of matrix W1+∞-algebras. We prove that they admit a PBW-type basis, establish a connection (limit construction) between these two types of algebras and toroidal quantum algebras, and we give three equivalent definitions of deformed double current algebras. We construct a Schur-Weyl functor between these algebras and rational Cherednik algebras. 相似文献
18.
S. Pumplün 《代数通讯》2013,41(6):2335-2366
We construct cubic Jordan algebras over an integral proper scheme X such that 2, 3 ∈ H 0(X, 𝒪 X ), generalizing a construction by B. N. Allison and J. R. Faulkner. In the process, we obtain admissible cubic algebras and pseudocomposition algebras over X. Results on the structure of these algebras are obtained, as well as examples over elliptic curves. 相似文献
19.
We study several families of semisimple Hopf algebras, arising as bismash products, which are constructed from finite groups with a certain specified factorization. First we associate a bismash product Hq of dimension q(q−1)(q+1) to each of the finite groups PGL2(q) and show that these Hq do not have the structure (as algebras) of group algebras (except when q=2,3). As a corollary, all Hopf algebras constructed from them by a comultiplication twist also have this property and are thus non-trivial. We also show that bismash products constructed from Frobenius groups do have the structure (as algebras) of group algebras. 相似文献
20.
Cristián Mallol 《代数通讯》2017,45(8):3486-3493
We study the relationship of backcrossing algebras with mutation algebras and algebras satisfying ω-polynomial identities: we show that in a backcrossing algebra every element of weight 1 generates a mutation algebra and that for any polynomial identity f there is a backcrossing algebra satisfying f. We give a criterion for the existence of idempotent in the case of baric algebras satisfying a nonhomogeneous polynomial identity and containing a backcrossing subalgebra. We give numerous genetic interpretations of the algebraic results. 相似文献