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GASTÓN ANDRÉS GARCÍA

Professor FCE-UNLP
Researcher CONICET


INFO

I am Adjunct Professor at the Math. Deparment at Universidad Nacional de La Plata and a Researcher of CONICET. My research field is non-commutative algebra. More specifically, Hopf algebras and quantum groups.


Hopf algebras were introduced in 50´s. From the 60´s they have been studied systematically, first in connection with algebraic groups and later as objects of self interest. Quantum groups, introduced in 1986 by Drinfeld, are a particular class of Hopf algebras that can be considered as deformations of universal enveloping algebras of Lie algebras or deformation of rings of regular functions on a Lie group.


My interest in quantum groups lie in the fact that they are a very important source of examples of Hopf algebras and must be taken into account to study the problem of classifying these algebras. In addition, quantum groups appear naturally codifying the symmetry of braided categories. In such a way they appear in various areas related to conformal field theory, for example, invariants of topological varieties of low dimension.


Photos / Fotos




Articles / Publikationen

G. A. García and F. Gavarini . Multiparameter quantum groups at roots of unity.
Preprint: abstract and file.

N. Andruskiewitsch, G. Carnovale and G. A. García. Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type IV. Unipotent classes in Chevalley and Steinberg groups.
Preprint: abstract and file.

F. Fantino, G. A. García and M. Mastnak. On finite-dimensional copointed Hopf algebras over dihedral groups.
Preprint: abstract and file.

G. A. García and J. M. Jury Giraldi. On Hopf algebras over quantum subgroups.
Preprint: abstract and file.

G. A. García and J. A. Gutiérrez. Quantum subgroups of simple twisted quantum groups at roots of one. Transactions of the AMS, to appear.
Preprint: abstract and file.

N. Andruskiewitsch, G. Carnovale and G. A. García. Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type III. Semisimple classes in PSL(n,q). Rev. Mat. Iberoam., to appear.


N. Andruskiewitsch, G. Carnovale and G. A. García. Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type II. Unipotent classes in symplectic groups. Comm. Contemp. Math. Vol. 18, No. 4 (2016) 1550053 (35 pages), On-line. Preprint: abstract and file.
Ktulu (He's so heavy) by Beatallica.

G. A. García. Multiparameter quantum groups, bosonizations and cocycle deformations. Rev. Un. Mat. Argentina, Vol. 57, no. 2 (2016), 1-23.

N. Andruskiewitsch, G. Carnovale and G. A. García. Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type I. Non-semisimple classes in PSL(n,q), J. Algebra 442 (2015), 36--65. On-line Preprint: abstract and file.
The call of cthulhu by Metallica.

G. A. García and M. Mastnak. Deformation by cocycles of pointed Hopf algebras over non-abelian groups, Math. Res. Lett. 22 (2015), 59--92. 
On line. Preprint: abstract and file.

M. Beattie and G. A. García. Classifying Hopf algebras of a given dimension.
Contemp. Math. 585 (2013), 125--152. Preprint: abstract and file.

M. Beattie and G. A. García. Techniques for classifying Hopf algebras and applications to dimension p3.
Comm. Algebra, 41 (2013), 3108–3129. On-line. Preprint: abstract and file.

N. Andruskiewitsch, F. Fantino G. A. García and L. Vendramín. On Nichols algebras associated to simple racks.
Contemp. Math. 537 (2011), 31--56. Preprint: abstract and file.

F. Fantino and G. A. García. On pointed Hopf algebras over dihedral groups. 
Pacific J. Math, Vol. 252 (2011), no. 1, 69--91. On line. Preprint: abstract and file. 23 pp.

G. A. García and A. García Iglesias. Finite dimensional pointed Hopf algebras over S4.
Israel J. Math. 183 (2011), 417--444. On line. Preprint: abstract and file.

N. Andruskiewitsch, F. Fantino G. A. García and L. Vendramín. On twisted homogeneous racks of type D.
Rev. Un. Mat. Argentina 51, no. 2 (2010), 1--16. On line. Preprint: abstract and file.

G. A. García. Quantum subgroups of GLa,b(n). 
J. Algebra 324 (2010), 1392–1428. On line. Preprint: abstract and file.

G. A. García and C.Vay. Hopf algebras of dimension 16.
Algebr. Represent. Theory 13, no. 4 (2010), 383--405. Online first. Preprint: abstract and file.

N. Andruskiewitsch and G. A. García. Finite subgroups of a simple quantum group.
Compositio Math. 145, no. 2 (2009), 476--500. Preprint: abstract and file.

N. Andruskiewitsch and G. A. García. Extensions of finite quantum groups by finite groups.
Tranformation Groups 14, no. 1 (2009), 1--27. Online first. Preprint: abstract and file.

G. A. García. On Hopf algebras of dimension p3.
Tsukuba J. Math. 29 (2005), no. 1, 259--284. Preprint: abstract and file.

Otros / Others / Anderes

Curso en VII Jornadas de Álgebra: Grupos cuánticos matriciales.



Curso en elENA IV: Números p-ádicos.


SOCIAL

DIRECCIÓN
Calle 50 y 115
Departamento de Matemática
Facultad de Ciencias Exactas
Universidad Nacional de La Plata
C.C. 172
1900 La Plata, Pcia. de Buenos Aires
República Argentina

CONTACTO
Email: ggarcia@mate.unlp.edu.ar
orcid
Scopus Author ID: 25642709600
ResearchGate
Tel/FAX: +54 221 424-5875
422- 9476/9850