ON ITERATED TWISTED TENSOR PRODUCTS OF ALGEBRAS

By Pascual JARA MARTÍNEZ, J. L. Peña, Florin Panaite, F. van Oystaeyen. 2005

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We introduce and study the definition, main properties and applications of iterated twisted tensor products of algebras, motivated by the problem of defining a suitable representative for the product of spaces in noncommutative geometry. We find conditions for constructing an iterated product of three factors and prove that they are enough for building an iterated product of any number of factors. As an example of the geometrical aspects of our construction, we show how to construct differential forms and involutions on iterated products starting from the corresponding structures on the factors and give some examples of algebras that can be described within our theory. We prove a certain result (called "invariance under twisting") for a twisted tensor product of two algebras, stating that the twisted tensor product does not change when we apply certain kind of deformation. Under certain conditions, this invariance can be iterated, containing as particular cases a number of independent and previously unrel...

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e7b480f2fb5789e0cf8c0f2642b8d66ccd7057e0

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In Algebra and Number Theory

  1. S. P. Smith
  2. Edwin J. Beggs
  3. Roozbeh Hazrat
  4. Xiao-Wu Chen

In Geometry and Topology

  1. S. P. Smith
  2. Edwin J. Beggs
  3. Roozbeh Hazrat
  4. Xiao-Wu Chen

In Mathematical Physics

  1. S. P. Smith
  2. Edwin J. Beggs
  3. Roozbeh Hazrat
  4. Xiao-Wu Chen

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