On Finite GK-Dimensional Nichols Algebras Over Abelian Groups (Memoirs of the American Mathematical Society) - Softcover

Andruskiewitsch, Nicolas; Angiono, Ivan; Heckenberger, Istvan

 
9781470448301: On Finite GK-Dimensional Nichols Algebras Over Abelian Groups (Memoirs of the American Mathematical Society)
Softcover
ISBN 10: 1470448300 ISBN 13: 9781470448301
Verlag: American Mathematical Society, 2021

Inhaltsangabe

"We contribute to the classification of Hopf algebras with finite Gelfand-Kirillov dimension, GKdim for short, through the study of Nichols algebras over abelian groups. We deal first with braided vector spaces over Z with the generator acting as a single Jordan block and show that the corresponding Nichols algebra has finite GKdim if and only if the size of the block is 2 and the eigenvalue is 1; when this is 1, we recover the quantum Jordan plane. We consider next a class of braided vector spaces that are direct sums of blocks and points that contains those of diagonal type. We conjecture that a Nichols algebra of diagonal type has finite GKdim if and only if the corresponding generalized root system is finite. Assuming the validity of this conjecture,we classify all braided vector spaces in the mentioned class whose Nichols algebra has finite GKdim. Consequently we present several new examples of Nichols algebras with finite GKdim, including two not in the class alluded to above. We determine which among these Nichols algebras are domains"--

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Über die Autorin bzw. den Autor

Nicolas Andruskiewitsch, Universidad Nacional de Cordoba, Argentina.

Ivan Angiono, Universidad Nacional de Cordoba, Argentina.

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Verlag
American Mathematical Society
Erscheinungsdatum
2021
Sprache
Englisch
ISBN 10 
1470448300
ISBN 13 
9781470448301
Einband
Tapa blanda
Anzahl der Seiten
127
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