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Introdução à álgebra de Hopf
(Universidade Tecnológica Federal do ParanáToledoBrasilLicenciatura em MatemáticaUTFPR, 2018-12-07)
The purpose of this work is to present the studies realized about algebras, coalgebras and bialgebras, culminating in the definition of Hopf algebras. Examples of each algebraic structures, as well as counterexamples when ...
Anéis semissimples e representações de grupo
(Universidade Tecnológica Federal do ParanáToledoBrasilLicenciatura em MatemáticaUTFPR, 2021-08-20)
The present work aims to present the theory of semisimple rings, group rings and group representations, in order to enable the calculation and to obtain the matrix representations of groups. This study is justified by the ...
The cohomology ring of the 12-dimensional Fomin-Kirillov algebra
(Academic Press Inc Elsevier Science, 2016-03)
The 12-dimensional Fomin-Kirillov algebra FK3 is defined as the quadratic algebra with generators a, b and c which satisfy the relations a2=b2=c2=0 and ab+bc+ca=0=ba+cb+ac. By a result of A. Milinski and H.-J. Schneider, ...
Galois orders in skew monoid rings
(ACADEMIC PRESS INC ELSEVIER SCIENCE, 2010)
We introduce a new class of noncommutative rings - Galois orders, realized as certain subrings of invariants in skew semigroup rings, and develop their structure theory. The class of Calms orders generalizes classical ...
Álgebras cuánticas de potencias divididas
(2016-03)
Se definen las álgebras de Lusztig y sus dobles de Drinfeld, las cuánticas de potencias divididas, asociadas a álgebras de Nichols de tipo diagonal de dimensión finita.
En ambos casos se prueba una presentación por ...