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Quasi-Commutative Algebras

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Abstract

We characterise algebras commutative with respect to a Yang-Baxter operator (quasi-commutative algebras) in terms of certain cosimplicial complexes. In some cases this characterisation allows the classification of all possible quasi-commutative structures.

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References

  1. Batanin, M.: Monoidal globular categories as a natural environment for the theory of weak n-categories. Adv. Math. 136(1), 39–103 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  2. Batanin, M., Street, R.: The universal property of the multitude of trees. Category theory and its applications (Montreal, QC, 1997). J. Pure Appl. Algebra 154(1–3), 3–13 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  3. Day, B., Street, R.: Abstract substitution in enriched categories. J. Pure Appl. Algebra 179(1–2), 49–63 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  4. Drinfel’d, V.G.: On some unsolved problems in quantum group theory. Quantum groups (Leningrad, 1990). In: Lecture Notes in Math., vol. 1510, pp. 1–8. Springer, Berlin (1992)

    Google Scholar 

  5. Etingof, P., Schedler, T., Soloviev, A.: Set-theoretical solutions to the quantum Yang-Baxter equation. Duke Math. J. 100(2), 169–209 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  6. Joyal, A.: Disks, duality and Θ-categories. Preprint and talk at the AMS Meeting in Montreal, September (1997)

  7. Joyal, A., Street, R.: The geometry of tensor calculus. I. Adv. Math. 88(1), 55–112 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  8. Lavers, T.G.: The theory of vines. Comm. Algebra 25(4), 1257–1284 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  9. Manin, Yu.: Quantum groups and non-commutative differential geometry. In: Mathematical Physics, X (Leipzig, 1991), pp. 113–122. Springer, Berlin (1992)

    Google Scholar 

  10. Lawvere, W.: Functorial semantics of algebraic theories. Proc. Natl. Acad. Sci. U. S. A. 50, 869–872 (1963)

    Article  MATH  MathSciNet  Google Scholar 

  11. Lu, J.-H., Yan, M., Zhu, Y.-C.: On the set-theoretical Yang-Baxter equation. Duke Math. J. 104(1), 1–18 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  12. MacLane, S.: Categorical algebra. Bull. Amer. Math. Soc. 71, 40–106 (1965)

    Article  MATH  MathSciNet  Google Scholar 

  13. MacLane, S.: Categories for the working mathematician. In: Graduate Texts in Mathematics, vol. 5, p. 262. Springer, New York (1971)

    Google Scholar 

  14. Montgomery, S.: Hopf Algebras and their Actions on Rings. American Mathematical Society, Providence, p. 238 (1993)

    MATH  Google Scholar 

  15. Street, R.: Higher categories, strings, cubes and simplex equations. Appl. Categ. Structures 3(1), 29–77 (1995)

    Article  MATH  MathSciNet  Google Scholar 

  16. Sweedler, M.: Hopf Algebras, p. 336. Benjamin, New York (1969)

    Google Scholar 

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Authors and Affiliations

  1. Macquarie University, Sydney, Australia

    A. Davydov

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  1. A. Davydov
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Correspondence to A. Davydov.

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Davydov, A. Quasi-Commutative Algebras. Appl Categor Struct 18, 377–406 (2010). https://doi.org/10.1007/s10485-008-9172-1

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  • DOI: https://doi.org/10.1007/s10485-008-9172-1

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