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61.
Noncommutative associative algebras are constructed which have the structure of module algebras over tensor products of pairs of quantized universal enveloping algebras. These module algebras decompose into multiplicity free direct sums of irreducible modules, yielding quantum analogues of generalized Howe dualities. 相似文献
62.
Let f(x) = aixi be a monic polynomial of degree n whosecoefficients are algebraically independent variables over a base field k of characteristic 0. We say that a polynomial g(x) isgenerating (for the symmetric group) if it can be obtained from f(x) by a nondegenerate Tschirnhaus transformation. We show that the minimal number dk(n) of algebraically independent coefficients of such a polynomial is at least [n/2]. This generalizes a classical theorem of Felix Klein on quintic polynomials and is related to an algebraic form of Hilberts 13th problem.Our approach to this question (and generalizations) is basedon the idea of the essential dimension of a finite group G:the smallest possible dimension of an algebraic G-variety over k to which one can compress a faithful linear representation of G. We show that dk(n) is just the essential dimension of the symmetricgroup Sn. We give results on the essential dimension ofother groups. In the last section we relate the notion of essential dimension to versal polynomials and discuss their relationship to the generic polynomials of Kuyk, Saltman and DeMeyer. 相似文献
63.
Honglian Zhang 《代数通讯》2013,41(11):3683-3698
The quantum affine algebra has two realizations, the usual Drinfeld–Jimbo definition and a new Drinfeld realization given by Drinfeld. In this article, we use the adjoint action to prove that these two realizations are isomorphic for the twisted quantum affine algebra. 相似文献
64.
We provide estimates for the fixed point ratios in the permutation representations of a finite classical group over a field of order q on k-subspaces of its natural n-dimensional module. For sufficiently large n, each element must either have a negligible ratio or act linearly with a large eigenspace. We obtain an asymptotic estimate in the latter case, which in most cases is q
–dk where d is the codimension of the large eigenspace. The results here are tailored for our forthcoming proof of a conjecture of Guralnick and Thompson on composition factors of monodromy groups. 相似文献
65.
In this paper we consider the transfer of the property of being a left Goldie ring between a ring A and its partial crossed product A*α G by a twisted partial action α of a group G on A. 相似文献
66.
Laurent Poinsot 《Discrete Applied Mathematics》2009,157(8):1848-1857
The left-regular multiplication is explicitly embedded in the notion of perfect nonlinearity. But there exist many other group actions. By replacing translations by another group action the new concept of group action-based perfect nonlinearity has been introduced. In this paper we show that this generalized concept of nonlinearity is actually equivalent to a new bentness notion that deals with functions defined on a finite Abelian group G that acts on a finite set X and with values in the finite-dimensional vector space of complex-valued functions defined on X. 相似文献
67.
Some rigidity results for non-commutative Bernoulli shifts 总被引:3,自引:0,他引:3
We introduce the outer conjugacy invariants , for cocycle actions σ of discrete groups G on type II1 factors N, as the set of real numbers t>0 for which the amplification σt of σ can be perturbed to an action, respectively, to a weakly mixing action. We calculate explicitly and the fundamental group of σ, , in the case G has infinite normal subgroups with the relative property (T) (e.g., when G itself has the property (T) of Kazhdan) and σ is an action of G on the hyperfinite II1 factor by Connes–Størmer Bernoulli shifts of weights {ti}i. Thus, and coincide with the multiplicative subgroup S of generated by the ratios {ti/tj}i,j, while if S={1} (i.e. when all weights are equal), and otherwise. In fact, we calculate all the “1-cohomology picture” of σt,t>0, and classify the actions (σ,G) in terms of their weights {ti}i. In particular, we show that any 1-cocycle for (σ,G) vanishes, modulo scalars, and that two such actions are cocycle conjugate iff they are conjugate. Also, any cocycle action obtained by reducing a Bernoulli action of a group G as above on to the algebra pNp, for p a projection in N, p≠0,1, cannot be perturbed to a genuine action. 相似文献
68.
Yves de Cornulier 《Geometriae Dedicata》2006,122(1):89-108
We characterize which permutational wreath products $G \ltimes W^{(X)}We characterize which permutational wreath products are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the cartesian square X
2. On the one hand, this extends a result of G. Baumslag about infinite presentation of standard wreath products; on the other
hand, this provides nontrivial examples of finitely presented groups. For instance, we obtain two quasi-isometric finitely
presented groups, one of which is torsion-free and the other has an infinite torsion subgroup. Motivated by the characterization
above, we discuss the following question: which finitely generated groups can have a finitely generated subgroup with finitely
many double cosets? The discussion involves properties related to the structure of maximal subgroups, and to the profinite
topology.
相似文献
69.
Oleg N. Ageev 《Proceedings of the American Mathematical Society》2006,134(5):1331-1338
We apply a technique to study the notion of spectral rigidity of group actions to a group gr. As an application, we prove that there exist rank one weakly mixing transformations conjugate to its square, thereby giving a positive answer to a well-known question.
70.
Yusuf Civan 《Proceedings of the American Mathematical Society》2006,134(5):1537-1548
We study the enumeration problem of stably complex structures on bounded flag manifolds arising from omniorientations, and determine those induced by almost complex structures. We also enumerate the stably complex structures on these manifolds which bound, therefore representing zero in the complex cobordism ring .