One-sided quantum quasigroups and loops

• Autorzy: Smith, J. D. H.
• Konferencja: Proceedings of the AAA88 - 88th Workshop on General Algebra Editors for the Special Issue: Anna Romanowska, Jonathan D. H. Smith
• Języki publikacji: EN

Abstrakty

EN

Quantum quasigroups and quantum loops are self-dual objects providing a general framework for the nonassociative extension of quantum group techniques. This paper examines their one-sided analogues, which are not self-dual. Just as quantum quasigroups are the “quantum” version of quasigroups, so one-sided quantum quasigroups are the “quantum” version of left or right quasigroups.

Słowa kluczowe

PL

algebra Hopfa; grupa kwantowa; quasi-grupa; pętla

EN

Hopf algebra; quantum group; right quasigroup; right loop

• Czasopismo: Demonstratio Mathematica
• Rocznik: 2015
• Tom: Vol. 48, nr 4
• Strony: 620--636
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Smith, J. D. H.

• Department of Mathematics, Iowa State University, Ames, Iowa 50011, U.S.A.,

Bibliografia

• [1] G. Benkart, S. Madaraga, J. M. Pérez-Izquierdo, Hopf algebras with triality, Trans. Amer. Math. Soc. 365 (2012), 1001–1023.
• [2] B. A. Davey, G. Davis, Tensor products and entropic varieties, Algebra Universalis 21 (1985), 68–88.
• [3] J. A. Green, W. D. Nichols, E. J. Taft, Left Hopf algebras, J. Algebra 65 (1980), 399–411.
• [4] J. Klim, S. Majid, Hopf quasigroups and the algebraic 7-sphere, J. Algebra 323 (2010), 3067–3110.
• [5] S. Majid, A Quantum Groups Primer, Cambridge University Press, Cambridge, 2002.
• [6] W. D. Nichols, E. J. Taft, The left antipodes of a left Hopf algebra, pp. 363–368 in Algebraists’ Homage, (S. A. Amitsur, D. J. Saltman and G. B. Seligman, eds.), Contemporary Mathematics 13, Amer. Math. Soc., Providence, RI, 1982.
• [7] J. M. Pérez-Izquierdo, Algebras, hyperalgebras, nonassociative bialgebras and loops, Adv. Math. 208 (2007), 834–876.
• [8] D. E. Radford, Hopf Algebras, World Scientific, Singapore, 2012.
• [9] S. Rodríguez-Romo, E. J. Taft, A left quantum group, J. Algebra 286 (2005), 154–160.
• [10] A. B. Romanowska, J. D. H. Smith, Entropic Hopf algebras, pp. 187–190 in TACL 2013. Sixth International Conference on Topology, Algebra and Categories in Logic, (N. Galatos, A. Kurz, C. Tsinakis, eds.), Easychair Proceedings in Computing 25, 2014. http://www.easychair.org/publications/?page=1060988868.
• [11] J. D. H. Smith, An Introduction to Quasigroups and Their Representations, Chapman and Hall/CRC, Boca Raton, FL, 2007.
• [12] J. D. H. Smith, Quantum quasigroups and loops, preprint, 2014.
• [13] J. D. H. Smith, A. B. Romanowska, Post-Modern Algebra, Wiley, New York, NY, 1999.
• [14] R. Street, Quantum Groups, Cambridge University Press, Cambridge, 2007.

Identyfikatory

DOI

10.1515/dema-2015-0043