共查询到20条相似文献,搜索用时 15 毫秒
1.
Mohan S. Putcha 《Semigroup Forum》2006,72(2):329-336
Let M be a finite monoid with unit group G such that J-related
idempotents in M are conjugate. If G is nilpotent, we prove that the complex
monoid algebra CM of M is semisimple if and only if M is an inverse
monoid. Conversely let G be a finite group such that for any finite
idempotent-conjugate monoid M with unit group G, CM semisimple implies
that M is an inverse monoid. We then show that G is a nilpotent group. 相似文献
2.
A two-parameter quantum group is obtained from the usual enveloping algebra by adding two commutative grouplike elements. In this paper, we generalize this procession further by adding commutative grouplike elements b_(ik), c_(ik), g_(ik), h_(ik)(i ∈I, k = 1,..., mi) of a Hopf algebra H to the quantized enveloping algebra U_q(G) of a Borcherds superalgebra G defined by a symmetrizable integral Borcherds–Cartan matrix A =(aij)i,j∈I. Therefore, we define an extended Hopf superalgebra HU_q(G). We also discuss the basis and the grouplike elements of HU_q(G). 相似文献
3.
4.
In this paper we prove the fundamental theorem of algebra for polynomials with coefficients in the skew field of Hamilton
numbers (quaternions) and in the division algebra of Cayley numbers (octonions). The proof, inspired by recent definitions
and results on regular functions of a quaternionic and of a octonionic variable, follows the guidelines of the classical topological
argument due to Gauss.
G. Gentili and F. Vlacci are partially supported by G.N.S.A.G.A. of the I.N.D.A.M. and by M.I.U.R. 相似文献
5.
JIANG Lining Department of Mathematics Beijing Institute of Technology Beijing China 《中国科学A辑(英文版)》2005,48(1)
In two-dimensional lattice spin systems in which the spins take values in afinite group G,one can define a field algebra F which carries an action of a Hopf algebraD(G),the double algebra of G and moreover,an action of D(G;H),which is a subalgebraof D(G)determined by a subgroup H of G,so that F becomes a modular algebra.Theconcrete construction of D(G;H)-invariant subspace A_H in F is given.By constructingthe quasi-basis of conditional expectation γ_G of A_H onto A_G,the C~*-index of γ_G is exactlythe index of H in G. 相似文献
6.
对一已知代数进行扩张,并研究扩张代数、重复代数与其模范畴之间的关系.首先利用代数A的双边理想I构造扩张代数T(A,I)和重复代数T(A,I),并研究其模范畴;其次研究范畴T(A,I)-Mod与T(A,I)-Mod的关系,得到于Tv(A,I)-Mod同构于T(A,I)-mod;另外证明存在T(A,I)-mod到T(A,I)-mod的覆盖函子;最后研究商代数A/I的平凡扩张代数T(A/I),得出T(A/I)/I与扩张代数T(A,I)同构. 相似文献
7.
Robyn Curtis 《Comptes Rendus Mathematique》2002,334(1):31-35
We define the Hecke von Neumann algebra associated with a group G, a subgroup H and a unitary representation σ of H. We show that when σ is finite dimensional, can be seen as a corner algebra of the tensor product of the group von Neumann algebra of a locally compact group and a matrix algebra. To cite this article: R. Curtis, C. R. Acad. Sci. Paris, Ser. I 334 (2002) 31–35 相似文献
8.
In the present paper, it is shown that a left cancellative
semigroup S (not necessarily with identity) is left amenable
whenever the Banach algebra ℓ1(S) is approximately amenable. It is also proved that if S is a Brandt semigroup over a group
G with an index set I, then ℓ1(S) is approximately
amenable if and only if G is amenable. Moreover ℓ1(S) is amenable if and only if G is amenable and I is finite. For a
left cancellative foundation semigroup S with an identity such
that for every Ma(S)-measurable subset B of S
and s ∈ S the set sB is Ma(S)-measurable,
it is proved that if the measure algebra Ma(S) is approximately
amenable, then S is left amenable. Concrete examples are given
to show that the converse is negative. 相似文献
9.
We consider a Lie ring (algebra) L that admits an automorphism φ of order 4 with a finite number m of fixed points (with a fixed-point subalgebra of finite dimension m). It is proved that L contains a subring S of m-bounded index in the additive group L (a subalgebra S of m-bounded codimension), which possesses a nilpotent ideal I of class bounded by some constant, such that the factor-ring S/I is nilpotent of class ≤2. As a consequence, it is proved that, under the same conditions, L has a subring G of m-bounded index in the additive group of L (a subalgebra G of m-bounded codimension), in which an ideal generated by the Lie subring [G, ?2]=«ng?g+g? 2 | g∈G»ng (the subalgebra [G, ?2]=«ng?g+g? 2 | g∈G»ng is an ideal in G which) is nilpotent of class bounded by some constant (and its factor-algebra G/[G, ?2] is nilpotent of class ≤2 with a derived algebra (square) of m-bounded dimension). In proofs, we use the results of [1] and develop further the version of the method of generalized centralizers employed therein. 相似文献
10.
设A是由箭图Q和关系I所确定的代数,D(A)是代数A的对偶扩张代数, 对应的箭图Q*和关系I*由Q和I决定.本文证明:带关系箭图(Q*,I*)的自同构由带关系箭图(Q,I)的自同构决定;D(A)的Frobenius态射由A的Frobenius态射完全决定;代数D(A)的固定点代数同构于相应的代数A的固定点代数与A°P的固定点代数的张量积,特别地,当Q为单的箭图时,代数D(A)的固定点代数同构于代数A的固定点代数的对偶扩张代数. 相似文献
11.
Given a simple graph G without loops and a field F of characteristic not 2 wr construct an exceptional Bernstein algebra F(G)over F and show that F(G)is indecomposable if and only if G is connected. The duplicate of F(G) is a Bernstein Jordan algebra whose type is deter- mined by the number of points and lines of G. We comment briefly how to extend the theory to the case of multigraphs. 相似文献
12.
We propose an inductive approach to the representation theory of the chain of complex reflection groups G(m, 1, n). We obtain the Jucys-Murphy elements of G(m, 1, n) from the Jucys-Murphy elements of the cyclotomic Hecke algebra and study their common spectrum using representations of a degenerate cyclotomic affine Hecke algebra. We construct representations of G(m, 1, n) using a new associative algebra whose underlying vector space is the tensor product of the group ring ?G(m, 1, n) with a free associative algebra generated by the standard m-tableaux. 相似文献
13.
G-旋模型场代数中的对偶定理 总被引:2,自引:0,他引:2
设G是有限群, H是G的子群,D(G)为G的Double代数, F是 G-旋模型所对应的场代数. 本文考虑D(G)的Hopf子代数D(H),证明了F的D(H)不变子空间AH是C*-代数.D(H)存在C*-表示,使得D(H)和AH互为换位子. 相似文献
14.
Volker Puppe 《manuscripta mathematica》1978,23(4):343-354
Under certain conditions the cohomology algebra (with appropriate coefficients) of the fixed point set of a G-space (G=Z/pZ=Zp, p prime or G=S1) can be considered a deformation - in a purely algebraic sense - of the cohomology algebra of the space itself. On one hand this gives restrictions on the isomorphism type of algebras that can occur as cohomology algebra of the fixed point set of G-spaces if the cohomology algebra of the space itself is given. On the other hand it leads to the definition of obstructions for the cohomology algebra of the fixed point set to be isomorphic (as an ungraded algebra) to the cohomology algebra of the space itself. 相似文献
15.
Fei Xu 《Archiv der Mathematik》2014,103(3):235-253
Let \({\mathcal{C}}\) be a finite EI category and k be a field. We consider the category algebra \({k\mathcal{C}}\) . Suppose \({\sf{K}(\mathcal{C})=\sf{D}^b(k \mathcal{C}-\sf{mod})}\) is the bounded derived category of finitely generated left modules. This is a tensor triangulated category, and we compute its spectrum in the sense of Balmer. When \({\mathcal{C}=G \propto \mathcal{P}}\) is a finite transporter category, the category algebra becomes Gorenstein, so we can define the stable module category \({\underline{\sf{CM}} k(G \propto \mathcal{P})}\) , of maximal Cohen–Macaulay modules, as a quotient category of \({{\sf{K}}(G \propto \mathcal{P})}\) . Since \({\underline{\sf{CM}} k(G\propto\mathcal{P})}\) is also tensor triangulated, we compute its spectrum as well. These spectra are used to classify tensor ideal thick subcategories of the corresponding tensor triangulated categories. 相似文献
16.
We prove that if A is an artin algebra, G is a finite group acting on A such that |G| is invertible in A, and R = A[G]b is a basic algebra associated with the skew group algebra, then A is left supported (or right supported, or laura, or left glued, or right glued, or weakly shod, or shod) if and only if so is R. 相似文献
17.
We prove that the stable endomorphism algebra of a module without self-extensions over a special biserial algebra is a gentle
algebra. In particular, it is again special biserial. As a consequence, any algebra which is derived equivalent to a gentle
algebra is gentle.
Received: 17 May 2002 /
Published online: 16 May 2003
Mathematics Subject Classification (2000): 16E30, 16G20, 18E30.
We gratefully acknowledge support from the Volkswagen Foundation (RIP Program at Oberwolfach). The first author thanks the
Nuffield Foundation (Grant Number NAL/00270/G) for financial support. 相似文献
18.
19.
Scott Annin 《Journal of Pure and Applied Algebra》2008,212(3):510-521
Attached primes and secondary representations were introduced in 1973 by Macdonald [I.G. Macdonald, Secondary representation of modules over a commutative ring, Sympos. Math. 11 (1973) 23-43] to develop a dual theory to the associated primes and primary decomposition in commutative algebra. This article generalizes Macdonald’s theory to the noncommutative setting. 相似文献
20.
Eduard A. Nigsch 《Mathematische Nachrichten》2013,286(10):1007-1021
We present a point value characterization for elements of the elementary full Colombeau algebra ${\mathcal {G}}^e(\Omega )$ and the diffeomorphism invariant full Colombeau algebra $\mathcal {G}^d(\Omega )$. Moreover, several results from the special algebra ${\mathcal {G}}^s(\Omega )$ about generalized numbers and invertibility are extended to the elementary full algebra. 相似文献