共查询到20条相似文献,搜索用时 15 毫秒
1.
Denote by D
m
the dihedral group of order 2m. Let ℛ(D
m
) be its complex representation ring, and let Δ(D
m
) be its augmentation ideal. In this paper, we determine the isomorphism class of the n-th augmentation quotient Δ
n
(D
m
)/Δ
n+1(D
m
) for each positive integer n. 相似文献
2.
Denote by \(C_m\) the cyclic group of order m. Let \({\mathcal {R}}(C_m)\) be its real representation ring, and \(\Delta (C_m)\) its augmentation ideal. In this paper, we give an explicit \({\mathbb {Z}}\)-basis for the n-th power \(\Delta ^{n}(C_m)\) and determine the isomorphism class of the n-th augmentation quotient \(\Delta ^n(C_m)/\Delta ^{n+1}(C_m)\) for each positive integer n. 相似文献
3.
4.
Consider a non-connected algebraic group G = G ⋉ Γ with semisimple identity component G and a subgroup of its diagram automorphisms Γ. The identity component G acts
on a fixed exterior component Gτ, id ≠ τ ∈ Γ by conjugation. In this paper we will describe the conjugacy classes and the
invariant theory of this action. Let T be a τ -stable maximal torus of G and its Weyl group W. Then the quotient space Gτ//G
is isomorphic to (T/(1 − τ )(T))/Wτ. Furthermore, exploiting the Jordan decomposition, the reduced fibres of this quotient map are naturally associated bundles
over semisimple G-orbits. Similar to Steinberg's connected and simply connected case [22] and under additional assumptions
on the fundamental group of G, a global section to this quotient map exists. The material presented here is a synopsis of
the Ph.D thesis of the author, cf. [15]. 相似文献
5.
6.
Emmanuel Breuillard Ben Green Robert Guralnick Terence Tao 《Israel Journal of Mathematics》2012,192(1):347-379
We show that (with one possible exception) there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski dense. As a consequence, we get new generating results for finite simple groups of Lie type and a strengthening of a theorem of Borel related to the Hausdorff-Banach-Tarski paradox. In a sequel to this paper, we use this result to also establish uniform expansion properties for random Cayley graphs over finite simple groups of Lie type 相似文献
7.
Mahir Bilen Can 《Journal of Algebra》2012,351(1):235-250
Let Λ be the cross section lattice of an irreducible representation of a semisimple algebraic group. Certain combinatorial properties of Λ are studied. Supersolvable Λ?s are determined in terms of Dynkin diagrams. The characteristic polynomial of a supersolvable Λ is computed. 相似文献
8.
9.
10.
S. Senthamarai Kannan 《Proceedings Mathematical Sciences》1999,109(3):241-256
We prove that ifG is a semisimple algebraic group of adjoint type over the field of complex numbers,H is the subgroup of all fixed points of an involution σ ofG that is induced by an involution σ of the simply connected coveringĜ ofG, then the wonderful compactification
of the homogeneous spaceG/H is isomorphic to the G.I.T quotientG
ss
(L)//H of the wonderful compactificationG ofG for a suitable choice of a line bundleL onG. We also prove a functorial property of the wonderful compactifications of semisimple algebraic groups of adjoint type. 相似文献
11.
A. S. Merkurjev 《Publications Mathématiques de L'IHéS》1996,84(1):189-213
The group of R-equivalence classes for all adjoint semisimple classical algebraic groups is computed. Examples of stably non-rational
adjoint simple groups of type D
n
,n≥3, are presented. The complete stable birational classification of adjoint simple groups of rank 3 is given.
This paper was written while the author was on sabbatical leave at the Université catholique de Louvain.
Typeset byA
M
S-TEX 相似文献
12.
We prove that the generic quantized coordinate ring q(G) isAuslander-regular, CohenMacaulay, and catenary for everyconnected semisimple Lie group G. This answers questions raisedby Brown, Lenagan, and the first author. We also prove thatunder certain hypotheses concerning the existence of normalelements, a noetherian Hopf algebra is AuslanderGorensteinand CohenMacaulay. This provides a new set of positivecases for a question of Brown and the first author. 相似文献
13.
14.
O. B. Podkopaev 《Journal of Mathematical Sciences》2007,140(5):729-736
The K0 groups of simply connected semisimple algebraic groups are calculated. The triviality of the Chow groups CH1 and CH2 of such groups is obtained as a consequence. Bibliography: 14 titles.
__________
Translated from Zapiski Nauchnykh Seminarov POMI, Vol. 330, 2006, pp. 223–235. 相似文献
15.
Shan Chang 《Czechoslovak Mathematical Journal》2016,66(4):1165-1175
Let H be a finite abelian group of odd order, D be its generalized dihedral group, i.e., the semidirect product of C2 acting on H by inverting elements, where C2 is the cyclic group of order two. Let Ω (D) be the Burnside ring of D, Δ(D) be the augmentation ideal of Ω (D). Denote by Δn(D) and Qn(D) the nth power of Δ(D) and the nth consecutive quotient group Δn(D)/Δn+1(D), respectively. This paper provides an explicit Z-basis for Δn(D) and determines the isomorphism class of Qn(D) for each positive integer n. 相似文献
16.
17.
We show that the quantum coordinate ring of a semisimple groupis a unique factorisation domain in the sense of Chatters andJordan in the case where the deformation parameter q is a transcendentalelement. 相似文献
18.
19.
Eduardo Casas-Alvero 《Journal of Pure and Applied Algebra》2007,208(3):1055-1062
We give an algebraic proof of a theorem of H. Maugendre showing how the jacobian quotients of a pair of germs of plane curve may be computed from their simultaneous immerged resolution, thus proving in particular their topological invariance. 相似文献