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Nontriviality results for the characteristic algebra of a DGA

Published online by Cambridge University Press:  28 July 2016

GEORGIOS DIMITROGLOU RIZELL
GEORGIOS DIMITROGLOU RIZELL*
Affiliation:
Centre for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0WB. e-mail: g.dimitroglou@maths.cam.ac.uk
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Abstract

Assume that we are given a semifree noncommutative differential graded algebra (DGA for short) whose differential respects an action filtration. We show that the canonical unital algebra map from the homology of the DGA to its characteristic algebra, i.e. the quotient of the underlying algebra by the two-sided ideal generated by the boundaries, is a monomorphism. The main tool that we use is the weak division algorithm in free noncommutative algebras due to P. Cohn.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 162 , Issue 3 , May 2017 , pp. 419 - 433
Copyright
Copyright © Cambridge Philosophical Society 2016 

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