Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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ON HOPF ALGEBRAS IN ENTROPIC JÓNSSON-TARSKI VARIETIES

  • ROMANOWSKA, ANNA B. (FACULTY OF MATHEMATICS AND INFORMATION SCIENCES WARSAW UNIVERSITY OF TECHNOLOGY) ;
  • SMITH, JONATHAN D.H. (DEPARTMENT OF MATHEMATICS IOWA STATE UNIVERSITY)
  • Received : 2014.10.24
  • Published : 2015.09.30
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Abstract

Comonoid, bi-algebra, and Hopf algebra structures are studied within the universal-algebraic context of entropic varieties. Attention focuses on the behavior of setlike and primitive elements. It is shown that entropic $J{\acute{o}}nsson$-Tarski varieties provide a natural universal-algebraic setting for primitive elements and group quantum couples (generalizations of the group quantum double). Here, the set of primitive elements of a Hopf algebra forms a Lie algebra, and the tensor algebra on any algebra is a bi-algebra. If the tensor algebra is a Hopf algebra, then the underlying $J{\acute{o}}nsson$-Tarski monoid of the generating algebra is cancellative. The problem of determining when the $J{\acute{o}}nsson$-Tarski monoid forms a group is open.

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References

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  3. Hopf monoids in varieties vol.79, pp.2, 2018, https://doi.org/10.1007/s00012-018-0500-5