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Trends in Contemporary Mathematics pp 59–72Cite as

Exploring Noncommutative Algebras via Deformation Theory

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Abstract

This is an expository paper which explains how one can use deformation theory to construct new algebras from known ones, and study their properties.

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Notes

  1. 1.

    By “an algebra” we always mean an associative algebra with unit.

  2. 2.

    The word “flat” refers to the fact that A is a (topologically) flat module over K, i.e. the functor of completed tensor product with this module is exact.

  3. 3.

    Note that we don’t have to worry about the existence of a unit in A since a flat formal deformation of an algebra with unit always has a unit.

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Acknowledgements

This paper is based on my lecture at “Giornata IndAM”, Naples, June 7, 2005. I would like to thank the organizers, in particular Corrado De Concini and Paolo Piazza for this wonderful opportunity. I am also grateful to J. Stasheff for useful comments.

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Authors and Affiliations

  1. Department of Mathematics, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA

    Pavel Etingof

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  1. Pavel Etingof
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Correspondence to Pavel Etingof .

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Editors and Affiliations

  1. Istituto Nazionale di Alta Matematica "Francesco Severi", Roma, Italy

    Vincenzo Ancona

  2. Dipartimento di Matematica, Università degli Studi di Roma "Tor Vergata", Roma, Italy

    Elisabetta Strickland

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Etingof, P. (2014). Exploring Noncommutative Algebras via Deformation Theory. In: Ancona, V., Strickland, E. (eds) Trends in Contemporary Mathematics. Springer INdAM Series, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-05254-0_5

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