共查询到20条相似文献,搜索用时 15 毫秒
1.
Ghislain Fourier 《Advances in Mathematics》2009,222(3):1080-1293
We provide combinatorial models for all Kirillov-Reshetikhin crystals of nonexceptional type, which were recently shown to exist. For types , , we rely on a previous construction using the Dynkin diagram automorphism which interchanges nodes 0 and 1. For type we use a Dynkin diagram folding and for types , a similarity construction. We also show that for types and the analog of the Dynkin diagram automorphism exists on the level of crystals. 相似文献
2.
The Kirillov–Reshetikhin modules Wr,s are finite-dimensional representations of quantum affine algebras U’q labeled by a Dynkin node r of the affine Kac–Moody algebra
and a positive integer s. In this paper we study the combinatorial structure of the crystal basis B2,s corresponding to W2,s for the algebra of type D(1)n.
2000 Mathematics Subject Classification Primary—17B37; Secondary—81R10
Supported in part by the NSF grants DMS-0135345 and DMS-0200774. 相似文献
3.
Kailash C. Misra 《代数通讯》2013,41(4):1599-1614
4.
For an affine algebra of nonexceptional type in the large rank we show the fermionic formula depends only on the attachment of the node 0 of the Dynkin diagram to the rest, and the fermionic formula of not type A can be expressed as a sum of that of type A with Littlewood–Richardson coefficients. Combining this result with Kirillov et al. (2002) [13] and Lecouvey et al. (2011) [18] we settle the X=M conjecture under the large rank hypothesis. 相似文献
5.
Andrea Jedwab 《代数通讯》2013,41(9):3456-3468
We introduce an invariant for the irreducible representations of finite dimensional Hopf algebras, defined as the trace of a map induced by the antipode on the endomorphisms of each corresponding simple module. We also compute the value of this invariant for the representations of two families of non-semisimple Hopf algebras. 相似文献
6.
J. Lurie 《Commentarii Mathematici Helvetici》2001,76(3):515-575
In this paper we adapt a known construction for the simply laced, semisimple Lie algebras (over Z), and thereby obtain a very simple construction for all minuscule representations of those Lie algebras (again over Z). We apply these results to give explicit formulas for tensors invariant under the exceptional algebras and .
Received: November 3, 2000 相似文献
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Hader A. Elgendy 《代数通讯》2013,41(4):1785-1810
We construct universal associative envelopes for the nonassociative triple systems arising from the trilinear operations of Bremner and Peresi applied to the 2-dimensional simple associative triple system. We use noncommutative Gröbner bases to determine monomial bases, structure constants, and centers of the universal envelopes. We show that the infinite dimensional envelopes are closely related to the down-up algebras of Benkart and Roby. For the finite dimensional envelopes, we determine the Wedderburn decompositions and classify the irreducible representations. 相似文献
9.
Sarah Rees 《Algebras and Representation Theory》2008,11(3):207-214
It is well known that the sets of strings that define all representations of string algebras and many representations of other
quotients of path algebras form a regular set, and hence are defined by finite state automata. This short article aims to
explain this connection between representation theory and automata theory in elementary terms; no technical background in
either representation theory or automata theory is assumed. The article describes the structure of the set of strings of a
monomial algebra as a locally testable and hence regular set, and describes explicitly the construction of the automaton,
illustrating the construction with an elementary example. Hence it explains how the sets of strings and bands of a monomial
algebra correspond to the sets of paths and closed (non-powered) circuits in a finite graph, and how the growth rate of the
set of bands is immediately visible from that graph.
Presented by C. Ringel. 相似文献
10.
Adam Hajduk 《代数通讯》2013,41(9):3236-3244
We introduce a concept generalizing classical degenerations of algebras (defined by structure constants) and Crawley-Boevey degenerations introduced in [3]. We prove that if A 0 is such a generalized degeneration of A 1 and the algebras have equal dimensions, then A 0 is a degeneration of A 1 in the classical sense. 相似文献
11.
Hader A. Elgendy 《代数通讯》2013,41(5):1827-1842
For n even, we prove Pozhidaev's conjecture on the existence of associative enveloping algebras for simple n-Lie (Filippov) algebras. More generally, for n even and any (n + 1)-dimensional n-Lie algebra L, we construct a universal associative enveloping algebra U(L) and show that the natural map L → U(L) is injective. We use noncommutative Gröbner bases to present U(L) as a quotient of the free associative algebra on a basis of L and to obtain a monomial basis of U(L). In the last section, we provide computational evidence that the construction of U(L) is much more difficult for n odd. 相似文献
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14.
Guillermo Cortiñas 《代数通讯》2013,41(3):1403-1412
Abstract Let D(H) be the quantum double associated to a finite dimensional quasi-Hopf algebra H, as in Hausser and Nill ((Hausser, F., Nill, F. (1999a). Diagonal crossed products by duals of quasi-quantum groups. Rev. Math. Phys. 11:553–629) and (Hausser, F., Nill, F. (1999b). Doubles of quasi-quantum groups. Comm. Math. Phys. 199:547–589)). In this note, we first generalize a result of Majid (Majid, S. (1991). Doubles of quasitriangular Hopf algebras. Comm. Algebra 19:3061–3073) for Hopf algebras, and then prove that the quantum double of a finite dimensional quasitriangular quasi-Hopf algebra is a biproduct in the sense of Bulacu and Nauwelaerts (Bulacu, D., Nauwelaerts, E. (2002). Radford's biproduct for quasi-Hopf algebras and bosonization. J. Pure Appl. Algebra 179:1–42.). 相似文献
15.
Michael Aschbacher Andrew M. Childs Paweł Wocjan 《Journal of Algebraic Combinatorics》2007,25(2):111-123
Mutually unbiased bases of a Hilbert space can be constructed by partitioning a unitary error basis. We consider this construction
when the unitary error basis is a nice error basis. We show that the number of resulting mutually unbiased bases can be at
most one plus the smallest prime power contained in the dimension, and therefore that this construction cannot improve upon
previous approaches. We prove this by establishing a correspondence between nice mutually unbiased bases and abelian subgroups
of the index group of a nice error basis and then bounding the number of such subgroups. This bound also has implications
for the construction of certain combinatorial objects called nets. 相似文献
16.
Ioannis Dokas 《代数通讯》2019,47(2):719-734
In this paper, we study A/k-bialgebras in prime characteristic. Firstly, we prove a Cartier type structure theorem for cocomplete A/k-bialgebras. Secondly, we generalize Michaelis’s theorem. In particular, we prove that a restricted (k, K)-Lie algebra is proper if and only if its restricted enveloping algebra is proper. 相似文献
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18.
I. A. Panin 《K-Theory》1994,8(6):541-585
The algebraicK-groups of projective homogeneous varieties are computed. The answer is given in terms ofK-groups of a semisimple algebra canonically associated with the variety. Our results generalize a result of Quillen and a result of Swan, whereK-groups of Severi-Brauer varieties and of smooth projective quadratic hypersurfaces were computed. 相似文献
19.
Let G be the group of points of a split reductive algebraic group G over a local field k and let X = G / U where U is the group of k-points of a maximal unipotent subgroup of G. In this paper we construct a certain canonical G-invariant space (called the Schwartz space of X) of functions on X, which is an extension of the space of smooth compactly supported functions on X. We show that the space of all elements of , which are invariant under the Iwahori subgroup I of G, coincides with the space generated by the elements of the so called periodic Lusztig basis, introduced recently by G. Lusztig
(cf. [10] and [11]). We also give an interpretation of this space in terms of a certain equivariant K-group (this was also
done by G. Lusztig — cf. [12]). Finally we present a global analogue of , which allows us to give a somewhat non-traditional treatment of the theory of the principal Eisenstein series. 相似文献
20.
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