Noncommutative Galois Extension and Graded q-Differential Algebra

We show that a semi-commutative Galois extension of a unital associative algebra can be endowed with the structure of a graded q -differential algebra. We study the first and higher order noncommutative differential calculus of semi-commutative Galois extension induced by the graded q -differential...

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Veröffentlicht in:	Advances in applied Clifford algebras 2016-03, Vol.26 (1), p.1-11
1. Verfasser:	Abramov, Viktor
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Mathematical and Computational Physics Mathematical Methods in Physics Physics Physics and Astronomy Theoretical
Online-Zugang:	Volltext
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Beschreibung
Zusammenfassung:	We show that a semi-commutative Galois extension of a unital associative algebra can be endowed with the structure of a graded q -differential algebra. We study the first and higher order noncommutative differential calculus of semi-commutative Galois extension induced by the graded q -differential algebra. As an example we consider the quaternions which can be viewed as the semi-commutative Galois extension of complex numbers.
ISSN:	0188-7009 1661-4909
DOI:	10.1007/s00006-015-0599-9