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19
The representation category of the quantum group of a nondegenerate bilinear form
 Comm. Algebra
"... We show that the representation category of the quantum group of a nondegenerate bilinear form is monoidally equivalent to the representation category of the quantum group SLq(2) for a wellchosen nonzero parameter q. The key ingredient for the proof of this result is the direct and explicit const ..."
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Cited by 14 (3 self)
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We show that the representation category of the quantum group of a nondegenerate bilinear form is monoidally equivalent to the representation category of the quantum group SLq(2) for a wellchosen nonzero parameter q. The key ingredient for the proof of this result is the direct and explicit construction of an appropriate Hopf bigalois extension. Then we get, when the base field is of characteristic zero, a full description of cosemisimple Hopf algebras whose representation semiring is isomorphic to the one of SL(2).
Fusion rules for representations of compact quantum groups
"... The compact quantum groups are objects which generalise at the same time the compact groups, the duals of discrete groups and the q−deformations (with q> 0) of classical compact Lie groups. A compact quantum group is an abstract object which may be described by (is by definition the dual of) the alg ..."
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Cited by 12 (6 self)
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The compact quantum groups are objects which generalise at the same time the compact groups, the duals of discrete groups and the q−deformations (with q> 0) of classical compact Lie groups. A compact quantum group is an abstract object which may be described by (is by definition the dual of) the algebra of “continuous functions
Poincaré Series of Quantum Spaces Associated to Hecke Operators
 Preprint ICTP 1997/171, qalg 9711020
, 1997
"... Abstract. We prove that the dimension of the homogeneous components of the quadratic algebras associated to a Hecke operator is a Pólya frequency (P) sequence. This result enables us to give some characterizations on the Poincaré series of these quadratic algebras. 1. ..."
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Cited by 11 (1 self)
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Abstract. We prove that the dimension of the homogeneous components of the quadratic algebras associated to a Hecke operator is a Pólya frequency (P) sequence. This result enables us to give some characterizations on the Poincaré series of these quadratic algebras. 1.
Characters o Representations of Quantum Groups of Type A_n
, 1998
"... We introduce the notion of characters of comodules over coribbon Hopf algebras. The case of quantum groups of type An is studied. We establish a characteristic equation for the quantum matrix and a qanalogue of HarishChandra ItzyksonZuber integral ..."
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Cited by 1 (0 self)
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We introduce the notion of characters of comodules over coribbon Hopf algebras. The case of quantum groups of type An is studied. We establish a characteristic equation for the quantum matrix and a qanalogue of HarishChandra ItzyksonZuber integral
Quantum Symmetric Functions And Characters Of Hecke Algebras
"... We introduce the notion of characters of comodules over coribbon Hopf algebras. We study in details the case of matrix quantum groups of type An . A quantum analog of CayleyHamilton equation for quantum matrix is proved. We show that for matrix quantum groups of type An , the ring of characters ..."
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We introduce the notion of characters of comodules over coribbon Hopf algebras. We study in details the case of matrix quantum groups of type An . A quantum analog of CayleyHamilton equation for quantum matrix is proved. We show that for matrix quantum groups of type An , the ring of characters is isomorphic to the ring of symmetric functions in an appropriate number of parameters. As a byproduct, we obtain a theory for characters of Hecke algebras.
INTEGRALS ON HOPF ALGEBRAS AND APPLICATION TO REPRESENTATION THEORY OF QUANTUM GROUPS OF TYPE A00
, 1999
"... In this work we study some properties of (noncosemisimple) Hopf algebras, possessing integrals, which are also called coFrobenius Hopf algebras. We apply the result obtained to the classification of representations of quantum groups of type A00. ..."
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In this work we study some properties of (noncosemisimple) Hopf algebras, possessing integrals, which are also called coFrobenius Hopf algebras. We apply the result obtained to the classification of representations of quantum groups of type A00.
ON THE REPRESENTATION CATEGORIES OF MATRIX QUANTUM GROUPS OF TYPE A
, 2005
"... Abstract. A quantum groups of type A is defined in terms of a Hecke symmetry. We show in this paper that the representation category of such a quantum group is uniquely determined as an abelian braided monoidal category by the birank of the Hecke symmetry. 1. ..."
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Abstract. A quantum groups of type A is defined in terms of a Hecke symmetry. We show in this paper that the representation category of such a quantum group is uniquely determined as an abelian braided monoidal category by the birank of the Hecke symmetry. 1.
THE INTEGRAL ON QUANTUM SUPER GROUPS OF TYPE Ars
, 1999
"... Abstract. We compute the integral on matrix quantum (super) groups of type A rs and derive from it the quantum analogue of (super) HCIZ integral. ..."
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Abstract. We compute the integral on matrix quantum (super) groups of type A rs and derive from it the quantum analogue of (super) HCIZ integral.
2 TEODOR BANICA
"... of “algebras of continuous functions on compact quantum groups ” and “C ∗algebras of ..."
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of “algebras of continuous functions on compact quantum groups ” and “C ∗algebras of
THE INTEGRAL ON QUANTUM SUPER GROUPS OF TYPE A rs PHÙNG HÔ ` HA ’ I
, 1998
"... Abstract. We compute the integral on matrix quantum (super) groups of type A rs and derive from it the quantum analogue of (super) HCIZ integral. ..."
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Abstract. We compute the integral on matrix quantum (super) groups of type A rs and derive from it the quantum analogue of (super) HCIZ integral.