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DEPARTMENT OF MATHEMATICS TECHNICAL REPORT
 

Summary: DEPARTMENT OF MATHEMATICS
TECHNICAL REPORT
COMPUTATION OF NON-COMMUTATIVE
GRšOBNER BASES IN
GRASSMANN AND CLIFFORD ALGEBRAS
DR. RAFAL ABLAMOWICZ
DECEMBER 2008
No. 2008-2
TENNESSEE TECHNOLOGICAL UNIVERSITY
Cookeville, TN 38505
Computation of Non-Commutative
Gršobner Bases in Grassmann and
Clifford Algebras
Rafal Ablamowicz
Abstract. Tensor, Clifford and Grassmann algebras belong to a wide class of
non-commutative algebras that have a PoincarŽe-Birkhoff-Witt (PBW) "mono-
mial" basis. The necessary and sufficient condition for an algebra to have the
PBW basis has been established by T. Mora and then V. Levandovskyy as
the so called "non-degeneracy condition". This has led V. Levandovskyy to
a re-discovery of the so called G-algebras (previously introduced by J. Apel)

  

Source: Ablamowicz, Rafal - Department of Mathematics, Tennessee Technological University

 

Collections: Mathematics