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Quantum Groups
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  • Cited by 22
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    This book has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Clementino, Maria Manuel Gran, Marino and Janelidze, George 2018. Some remarks on protolocalizations and protoadditive reflections. Journal of Algebra and Its Applications, Vol. 17, Issue. 11, p. 1850207.

    Böhm, Gabriella 2018. Hopf Algebras and Their Generalizations from a Category Theoretical Point of View. Vol. 2226, Issue. , p. 47.

    Duncan, Ross and Dunne, Kevin 2016. Interacting Frobenius Algebras are Hopf. p. 535.

    Gran, Marino Kadjo, Gabriel and Vercruysse, Joost 2016. A Torsion Theory in the Category of Cocommutative Hopf Algebras. Applied Categorical Structures, Vol. 24, Issue. 3, p. 269.

    Poinsot, Laurent and Porst, Hans-E. 2016. The Dual Rings of anR-Coring Revisited. Communications in Algebra, Vol. 44, Issue. 3, p. 944.

    Porst, Hans-E. and Street, Ross 2016. Generalizations of the Sweedler Dual. Applied Categorical Structures, Vol. 24, Issue. 5, p. 619.

    Porst, Hans-E. 2015. The formal theory of hopf algebras Part I: Hopf monoids in a monoidal category. Quaestiones Mathematicae, Vol. 38, Issue. 5, p. 631.

    Poinsot, Laurent and Porst, Hans-E. 2015. Free Monoids over Semigroups in a Monoidal Category: Construction and Applications. Communications in Algebra, Vol. 43, Issue. 11, p. 4873.

    Porst, Hans-E. 2015. The formal theory of Hopf algebras Part II: The case of Hopf algebras. Quaestiones Mathematicae, Vol. 38, Issue. 5, p. 683.

    Abuhlail, Jawad Y. and Al-Sulaiman, Nabeela 2015. Hopf Semialgebras. Communications in Algebra, Vol. 43, Issue. 3, p. 1241.

    Lawson, Mark V. and Wallis, Alistair R. 2015. A correspondence between a class of monoids and self-similar group actions II. International Journal of Algebra and Computation, Vol. 25, Issue. 04, p. 633.

    Gerhold, Malte and Lachs, Stephanie 2015. Classification and GNS-construction for general universal products. Infinite Dimensional Analysis, Quantum Probability and Related Topics, Vol. 18, Issue. 01, p. 1550004.

    Melliès, Paul-André 2013. Computation, Logic, Games, and Quantum Foundations. The Many Facets of Samson Abramsky. Vol. 7860, Issue. , p. 197.

    HASEGAWA, MASAHITO 2012. A quantum double construction in Rel. Mathematical Structures in Computer Science, Vol. 22, Issue. 04, p. 618.

    Coecke, Bob and Spekkens, Robert W. 2012. Picturing classical and quantum Bayesian inference. Synthese, Vol. 186, Issue. 3, p. 651.

    Porst, Hans-E. 2012. Free Internal Groups. Applied Categorical Structures, Vol. 20, Issue. 1, p. 31.

    Coecke, Bob Duncan, Ross Kissinger, Aleks and Wang, Quanlong 2012. Strong Complementarity and Non-locality in Categorical Quantum Mechanics. p. 245.

    Došen, Kosta and Petrić, Zoran 2012. Symmetric Self-adjunctions and Matrices. Algebra Colloquium, Vol. 19, Issue. spec01, p. 1051.

    Chikhladze, Dimitri 2012. The Tannaka Representation Theorem for Separable Frobenius Functors. Algebras and Representation Theory, Vol. 15, Issue. 6, p. 1205.

    Coecke, Bob and Edwards, Bill 2011. Three qubit entanglement within graphical Z/X-calculus. Electronic Proceedings in Theoretical Computer Science, Vol. 52, Issue. , p. 22.


Book description

Algebra has moved well beyond the topics discussed in standard undergraduate texts on 'modern algebra'. Those books typically dealt with algebraic structures such as groups, rings and fields: still very important concepts! However Quantum Groups: A Path to Current Algebra is written for the reader at ease with at least one such structure and keen to learn algebraic concepts and techniques. A key to understanding these new developments is categorical duality. A quantum group is a vector space with structure. Part of the structure is standard: a multiplication making it an 'algebra'. Another part is not in those standard books at all: a comultiplication, which is dual to multiplication in the precise sense of category theory, making it a 'coalgebra'. While coalgebras, bialgebras and Hopf algebras have been around for half a century, the term 'quantum group', along with revolutionary new examples, was launched by Drinfel'd in 1986.


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