53 citations · 216 across the 44 of their papers we have counts for
27 papers · 1 filter
Multiparameter quantum general linear supergroup
Fabio Gavarini, Margherita Paolini
We introduce uniparametric and multiparametric quantisations of the general linear supergroup, in the form of "quantised function algebras", both in a formal setting - yielding "qu…
Multiparameter Quantum Supergroups, Deformations and Specializations
Gastón Andrés García, Fabio Gavarini, Margherita Paolini
In this paper we introduce a multiparameter version of the quantum universal enveloping superalgebras introduced by Yamane in [H. Yamane, "Quantized enveloping algebras associated…
Quantum group deformations and quantum -(co)matrices vs. Quantum Duality Principle
Gastón Andrés García, Fabio Gavarini
In this paper we describe the effect on quantum groups -- namely, both QUEA's and QFSHA's -- of deformations by twist and by 2-cocycles, showing how such deformations affect the se…
Formal multiparameter quantum groups, deformations and specializations
Gastón Andrés García, Fabio Gavarini
We introduce the notion of formal multiparameter quantum universal enveloping algebras - in short FoMpQUEA - as a straightforward generalization of Drinfeld's quantum group. Then w…
Quantum Duality Principle for quantum continuous Kac-Moody algebras
Fabio Gavarini
For the quantized universal enveloping algebra U_h(g_X) associated with a continuous Kac-Moody algebra g_X as in [A. Appel, F. Sala, "Quantization of continuum Kac-Moody algebras",…
Twisted deformations vs. cocycle deformations for quantum groups
Gastón Andrés García, Fabio Gavarini
In this paper we study two deformation procedures for quantum groups: deformations by twists, that we call "comultiplication twisting", as they modify the coalgebra structure, whil…
Multiparameter quantum groups at roots of unity
Gastón Andrés García, Fabio Gavarini
We address the study of multiparameter quamtum groups (=MpQG's) at roots of unity, namely quantum universal enveloping algebras depending o…
Duality functors for quantum groupoids
Sophie Chemla, Fabio Gavarini
We present a formal algebraic language to deal with quantum deformations of Lie-Rinehart algebras - or Lie algebroids, in a geometrical setting. In particular, extending the ice-br…
A global quantum duality principle for subgroups and homogeneous spaces
Nicola Ciccoli, Fabio Gavarini
For a complex or real algebraic group G, with g:=Lie(G), quantizations of global type are suitable Hopf algebras F_q[G] or U_q(g) over C[q,q^{-1}]. Any such quantization yields a s…
The global quantum duality principle: a survey through examples
Fabio Gavarini
Let R be a 1-dimensional integral domain, let h (non-zero) be a prime element, and let \HA be the category of torsionless Hopf algebras over R. We call H in \HA a "quantized functi…
Quantization of Projective Homogeneous Spaces and Duality Principle
N. Ciccoli, R. Fioresi, F. Gavarini
We introduce a general recipe to construct quantum projective homogeneous spaces, with a particular interest for the examples of the quantum Grassmannians and the quantum generaliz…
PBW theorems and Frobenius structures for quantum matrices
Fabio Gavarini
Let G be either of Mat(n), GL(n) or SL(n), let O_q(G) be the quantum function algebra - over Z[q,q^{-1}] - associated to G, and let O_e(G) be the specialisation of O_q(G) at a root…
A PBW theorem for O_e(M_n), O_e(GL_n) and O_e(SL_n) over O(M_n), O(GL_n) and O(SL_n)
Fabio Gavarini
This paper has been withdrawn by the author. Its natural evolution is preprint math.QA/0610691, which is different enough to bear a different title (though they share about 2/3s of…
Quantum duality principle for coisotropic subgroups and Poisson quotients
Nicola Ciccoli, Fabio Gavarini
We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual: namely, starting from a quantum coisotropic subgroup (for a quantization…
Quantum Duality Principle for Quantum Grassmannians
Rita Fioresi, Fabio Gavarini
The quantum duality principle (QDP) for homogeneous spaces gives four recipes to obtain, from a quantum homogeneous space, a dual one, in the sense of Poisson duality. One of these…
A quantum duality principle for coisotropic subgroups and Poisson quotients
Nicola Ciccoli, Fabio Gavarini
We develop a quantum duality principle for coisotropic subgroups of a (formal) Poisson group and its dual. Namely, starting from a quantum coisotropic subgroup (for a quantization…
A Formula for the Logarithm of the KZ Associator
Benjamin Enriquez, Fabio Gavarini
We prove that the logarithm of a group-like element in a free algebra coincides with its image by a certain linear map. We use this result and the formula of Le and Murakami for th…
Presentation by Borel subalgebras and Chevalley generators for quantum enveloping algebras
Fabio Gavarini
We provide an alternative approach to the Faddeev-Reshetikhin-Takhtajan presentation of the quantum group U_q(g), with L-operators as generators and relations ruled by an R-matrix.…
A quantum duality principle for subgroups and homogeneous spaces
Nicola Ciccoli, Fabio Gavarini
We develop a quantum duality principle for subgroups of a Poisson group and its dual, in two formulations. Namely, in the first one we provide functorial recipes to produce quantum…
Poisson geometrical symmetries associated to non-commutative formal diffeomorphisms
Fabio Gavarini
Let G be the group of all formal power series starting with x with coefficients in a field k of zero characteristic (with the composition product), and let F[G] be its function alg…
The Crystal Duality Principle: from Hopf Algebras to Geometrical Symmetries
Fabio Gavarini
We give functorial recipes to get, out of any Hopf algebra over a field, two pairs of Hopf algebras which have some geometrical content. When the ground field has characteristic ze…
The global quantum duality principle: theory, examples, and applications
Fabio Gavarini
Let R be an integral domain, h non-zero in R such that R/hR is a field, and HA the category of torsionless (or flat) Hopf algebras over R. We call any H in HA "quantized function a…
Braiding structures on formal Poisson groups and classical solutions of the QYBE
Fabio Gavarini, Gilles Halbout
If g is a quasitriangular Lie bialgebra, one can asks what is the geometrical meaning of its r-matrix. A first answer was given in a paper by Weinstein and Xu, using purely geometr…
The global quantum duality principle: theory, examples, applications
Fabio Gavarini
The "quantum duality principle" states that a quantisation of a Lie bialgebra provides also a quantisation of the dual formal Poisson group and, conversely, a quantisation of a for…