375 research outputs found
PBW deformations of a Fomin-Kirillov algebra and other examples
We begin the study of PBW deformations of graded algebras relevant to the
theory of Hopf algebras. One of our examples is the Fomin-Kirillov algebra FK3.
Another one appeared in a paper of Garc\'ia Iglesias and Vay. As a consequence
of our methods, we determine when the deformations are semisimple and we are
able to produce PBW bases and polynomial identities for these deformations.Comment: 22 pages. Accepted for publication in Algebr. Represent. Theor
Bosonization of curved Lie bialgebras
We use Cartier's preadditive symmetric monoidal categories to study Lie
bialgebras. We prove that bosonization can be done consistently in this
framework. In the last part of the paper we present explicit examples and
indicate a deep relationship between certain curved Lie bialgebras and Nichols
algebras over abelian groups.Comment: 22 pages. Final version; postprin
PBW deformations of a Fomin–Kirillov Algebra and other examples
We begin the study of PBW deformations of graded algebras relevant to the theory of Hopf algebras. One of our examples is the Fomin–Kirillov algebra E3. Another one appeared in a paper of García Iglesias and Vay. As a consequence of our methods, we determine when the deformations are semisimple and we are able to produce PBW bases and polynomial identities for these deformations.Fil: Heckenberger, I.. Philipps-Universität Marburg; AlemaniaFil: Vendramin, Claudio Leandro. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentin
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