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Displaying 201 – 220 of 284

Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres

Elmar Wagner (2011)

Banach Center Publications

It is shown that the isospectral bi-equivariant spectral triple on quantum SU(2) and the isospectral equivariant spectral triples on the Podleś spheres are related by restriction. In this approach, the equatorial Podleś sphere is distinguished because only in this case the restricted spectral triple admits an equivariant grading operator together with a real structure (up to infinitesimals of arbitrary high order). The real structure is expressed by the Tomita operator on quantum SU(2) and it is...

Right coideal subalgebras of $U_{q}^{+} ({𝔰𝔬}_{2 n + 1})$

V. K. Kharchenko (2011)

Journal of the European Mathematical Society

We give a complete classification of right coideal subalgebras that contain all grouplike elements for the quantum group $U_{q}^{+} ({𝔰𝔬}_{2 n + 1})$ provided that $q$ is not a root of 1. If $q$ has a finite multiplicative order $t > 4$ ; this classification remains valid for homogeneous right coideal subalgebras of the Frobenius–Lusztig kernel $u_{q}^{+} ({𝔰𝔬}_{2 n + 1})$ . In particular, the total number of right coideal subalgebras that contain the coradical equals $(2 n)!!$ ; the order of the Weyl group defined by the root system of type $B_{n}$ .

Ringel-Hall algebras of hereditary pure semisimple coalgebras

Justyna Kosakowska (2009)

Colloquium Mathematicae

We define and investigate Ringel-Hall algebras of coalgebras (usually infinite-dimensional). We extend Ringel's results [Banach Center Publ. 26 (1990) and Adv. Math. 84 (1990)] from finite-dimensional algebras to infinite-dimensional coalgebras.

R-matrix brackets and their quantization

J. Donin, D. Gurevich, S. Majid (1993)

Annales de l'I.H.P. Physique théorique

Root vectors in quantum groups.

Nanhua Xi (1994)

Commentarii mathematici Helvetici

Rosso's form and quantized Kac Moody algebras.

Anthony Joseph, Gail Letzter (1996)

Mathematische Zeitschrift

Semicanonical bases and preprojective algebras

Christof Geiss, Bernard Leclerc, Jan Schröer (2005)

Annales scientifiques de l'École Normale Supérieure

Semi-centre de l'algèbre enveloppante d'une sous-algèbre parabolique d'une algèbre de Lie semi-simple

Florence Fauquant-Millet, Anthony Joseph (2005)

Annales scientifiques de l'École Normale Supérieure

Semilinear relations and *-representations of deformations of so(3)

Yuriĭ Samoĭlenko, Lyudmila Turowska (1997)

Banach Center Publications

We study a family of commuting selfadjoint operators $= {(A_{k})}_{k = 1}^{n}$ , which satisfy, together with the operators of the family $= {(B_{j})}_{j = 1}^{n}$ , semilinear relations $⅀_{i} f_{i j} () B_{j} g_{i j} () = h ()$ , ( $f_{i j}$ , $g_{i j}$ , $h_{j} : ℝ^{n} \to ℂ$ are fixed Borel functions). The developed technique is used to investigate representations of deformations of the universal enveloping algebra U(so(3)), in particular, of some real forms of the Fairlie algebra $U_{q}^{'} (s o (3))$ .

Separation of variables in the quantum integrable models related to the Yangian $𝒴 [\geq r m s l (3)]$

Е.К. Склянин (1993)

Zapiski naucnych seminarov POMI

Skein quantization of Poisson algebras of loops on surfaces

Vladimir G. Turaev (1991)

Annales scientifiques de l'École Normale Supérieure

Skein theory for $S U (n)$ -quantum invariants.

Sikora, Adam S. (2005)

Algebraic & Geometric Topology

Sklyanin determinant for reflection algebra.

Rozhkovskaya, Natasha (2010)

SIGMA. Symmetry, Integrability and Geometry: Methods and Applications [electronic only]

Smallness problem for quantum affine algebras and quiver varieties

David Hernandez (2008)

Annales scientifiques de l'École Normale Supérieure

The geometric small property (Borho-MacPherson [2]) of projective morphisms implies a description of their singularities in terms of intersection homology. In this paper we solve the smallness problem raised by Nakajima [37, 35] for certain resolutions of quiver varieties [37] (analogs of the Springer resolution): for Kirillov-Reshetikhin modules of simply-laced quantum affine algebras, we characterize explicitly the Drinfeld polynomials corresponding to the small resolutions. We use an elimination...

Solutions to the XXX type Bethe ansatz equations and flag varieties

E. Mukhin, A. Varchenko (2003)

Open Mathematics

We consider a version of the A N Bethe equation of XXX type and introduce a reporduction procedure constructing new solutions of this equation from a given one. The set of all solutions obtained from a given one is called a population. We show that a population is isomorphic to the sl N+1 flag variety and that the populations are in one-to-one correspondence with intersection points of suitable Schubert cycles in a Grassmanian variety. We also obtain similar results for the root systems B N and...

Solvable lattice model and representation theory of quantum affine algebras.

Miwa, Tetsuji (1998)

Documenta Mathematica

Some details of proofs of theorems related to the quantum dynamical Yang-Baxter equation.

Koornwinder, Tom H. (2000)

International Journal of Mathematics and Mathematical Sciences

Some exceptional compact matrix pseudogroups

Nicolás Andruskiewitsch (1992)

Bulletin de la Société Mathématique de France

Some remarks on quantum and braided group gauge theory

Shahn Majid (1997)

Banach Center Publications

We clarify some aspects of quantum group gauge theory and its recent generalisations (by T. Brzeziński and the author) to braided group gauge theory and coalgebra gauge theory. We outline the diagrammatic version of the braided case. The bosonisation of any braided group provides us a trivial principal bundle in three ways.

Spectrum of the quantized Weyl algebra. (Spectre de l'algèbre de Weyl quantique.)

Rigal, Laurent (1996)

Beiträge zur Algebra und Geometrie

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