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of 569
pro vyhledávání: '"Gavarini A"'
In this paper we introduce a multiparameter version of the quantum universal enveloping superalgebras introduced by Yamane in [H. Yamane, "Quantized enveloping algebras associated to simple Lie superalgebras and their universal $R$-matrices", Publ. R
Externí odkaz:
http://arxiv.org/abs/2410.22549
Autor:
García, Gastón Andrés, Gavarini, Fabio
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 semiclassical limit. As a second, more important task, we discuss how th
Externí odkaz:
http://arxiv.org/abs/2403.15096
Autor:
Chuah, Meng-Kiat, Gavarini, Fabio
We consider a real Abelian Lie supergroup $G$ acting on its complexification $M$, equipped with a $G$-invariant super K\"ahler form. We extend the scheme of classical geometric quantization to this setting and construct a unitary $G$-representation.
Externí odkaz:
http://arxiv.org/abs/2312.00444
Autor:
Ahmadilivani, Mohammad Hasan, Barbareschi, Mario, Barone, Salvatore, Bosio, Alberto, Daneshtalab, Masoud, Della Torca, Salvatore, Gavarini, Gabriele, Jenihhin, Maksim, Raik, Jaan, Ruospo, Annachiara, Sanchez, Ernesto, Taheri, Mahdi
Deep Learning, and in particular, Deep Neural Network (DNN) is nowadays widely used in many scenarios, including safety-critical applications such as autonomous driving. In this context, besides energy efficiency and performance, reliability plays a
Externí odkaz:
http://arxiv.org/abs/2306.04645
Autor:
García, Gastón Andrés, Gavarini, Fabio
We introduce the notion of formal multiparameter quantum universal enveloping algebras - in short FoMpQUEA - as a straightforward generalization of Drinfeld's quantum group. Then we show that the class of FoMpQUEA's is closed under deformations by ("
Externí odkaz:
http://arxiv.org/abs/2203.11023
Autor:
Gavarini, Fabio
Publikováno v:
Journal of Lie theory 32 (2022), no. 2, 839-862
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", Pure Appl. Math. Q. 16 (2020), no. 3, 439-493], we prove that a suita
Externí odkaz:
http://arxiv.org/abs/2202.06090
Autor:
Fioresi, Rita, Gavarini, Fabio
Publikováno v:
Communications in Mathematical Physics 397 (2023), no. 2, 937-965
We investigate the notion of real form of complex Lie superalgebras and supergroups, both in the standard and graded version. Our functorial approach allows most naturally to go from the superalgebra to the supergroup and retrieve the real forms as f
Externí odkaz:
http://arxiv.org/abs/2003.10535
Autor:
García, Gastón Andrés, Gavarini, Fabio
Publikováno v:
Communications in Contemporary Mathematics, Vol. 23 (2021), no. 8 - 2050084 (56 pages)
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, while keeping the algebra one -- and deformations by 2-cocycle, that we ca
Externí odkaz:
http://arxiv.org/abs/1807.01149
Autor:
Iohara, Kenji, Gavarini, Fabio
Publikováno v:
SIGMA 14 (2018), 137, 36 pages
The complex Lie superalgebras $\mathfrak{g}$ of type $D(2,1;a)$ - also denoted by $\mathfrak{osp}(4,2;a) $ - are usually considered for "non-singular" values of the parameter $a$, for which they are simple. In this paper we introduce five suitable in
Externí odkaz:
http://arxiv.org/abs/1709.04717
Autor:
García, Gastón Andrés, Gavarini, Fabio
Publikováno v:
J. Noncommut. Geom., 16 (2022), 839--926
We address the study of multiparameter quamtum groups (=MpQG's) at roots of unity, namely quantum universal enveloping algebras $ U_{\boldsymbol{\rm q}}(\mathfrak{g}) $ depending on a matrix of parameters $ \boldsymbol{\rm q} = {\big( q_{ij} \big)}_{
Externí odkaz:
http://arxiv.org/abs/1708.05760