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Algebra i Analiz, 2000, Volume 12, Issue 5, Pages 3–27 (Mi aa1120)  

This article is cited in 9 scientific papers (total in 9 papers)

Research Papers

Harmonic analysis on semisimple Hopf algebras

N. Andruskiewitsch, S. Natale

Ciudad Universitaria, FaMAF, Córdoba, Argentina

Abstract: Let $H$ be a semisimple Hopf algebra. The relationship is studied between the character algebra of $H$ and that of a Hopf subalgebra. Hecke algebras are discussed, as well as their links with quantum spaces of double cosets. An explicit expression for spherical functions is given. Also, Gelfand pairs are studied, and a description of Fourier analysis on symmetric spaces via spherical functions is presented. It is shown that the pair $(D(H), H)$ is a Gelfand pair if and only if $H$ is almost cocommutative; here $D(H)$ is the Drinfeld double of $H$.

Keywords: Coalgebra, quantum groups, Kac algebras, Gelfand pairs, Drinfeld double

Full text: PDF file (1132 kB)

English version:
St. Petersburg Mathematical Journal, 2001, 12:5, 713–732

Bibliographic databases:

Received: 24.12.1999
Language:

Citation: N. Andruskiewitsch, S. Natale, “Harmonic analysis on semisimple Hopf algebras”, Algebra i Analiz, 12:5 (2000), 3–27; St. Petersburg Math. J., 12:5 (2001), 713–732

Citation in format AMSBIB
\Bibitem{AndNat00}
\by N.~Andruskiewitsch, S.~Natale
\paper Harmonic analysis on semisimple Hopf algebras
\jour Algebra i Analiz
\yr 2000
\vol 12
\issue 5
\pages 3--27
\mathnet{http://mi.mathnet.ru/aa1120}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1812940}
\zmath{https://zbmath.org/?q=an:1011.16028}
\transl
\jour St. Petersburg Math. J.
\yr 2001
\vol 12
\issue 5
\pages 713--732


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Castaño Iglesias F., Dǎscǎlescu S., Nǎstǎsescu C., “Symmetric coalgebras”, J. Algebra, 279:1 (2004), 326–344  crossref  mathscinet  zmath  isi  scopus
    2. Mombelli J.M., “Dynamical twists in Hopf algebras”, Int. Math. Res. Not. IMRN, 2007, no. 13, rnm039, 25 pp.  crossref  mathscinet  zmath  isi  scopus
    3. Hu J., Zhang Y., “Induced modules of semisimple Hopf algebras”, Algebra Colloquium, 14:4 (2007), 571–584  crossref  mathscinet  zmath  isi
    4. Natale S., “Semisolvability of Semisimple Hopf Algebras of Low Dimension”, Memoirs of the American Mathematical Society, 186:874 (2007), 1  crossref  mathscinet  isi
    5. Dong J., Wang Sh., “On Semisimple Hopf Algebras of Dimension 2Q(3)”, J. Algebra, 375 (2013), 97–108  crossref  mathscinet  zmath  isi  scopus
    6. Cohen M., Westreich S., “Are We Counting Or Measuring Something?”, J. Algebra, 398 (2014), 111–130  crossref  mathscinet  zmath  isi  elib  scopus
    7. Cohen M., Westreich S., “Solvability for semisimple Hopf algebras via integrals”, J. Algebra, 472 (2017), 67–94  crossref  mathscinet  zmath  isi  elib  scopus
    8. Shimizu K., “the Monoidal Center and the Character Algebra”, J. Pure Appl. Algebr., 221:9 (2017), 2338–2371  crossref  mathscinet  zmath  isi  elib  scopus
    9. Aldenhoven N., Koelink E., Roman P., “Matrix-Valued Orthogonal Polynomials Related to the Quantum Analogue of (Su (2) X Su(2), Diag)”, Ramanujan J., 43:2 (2017), 243–311  crossref  mathscinet  zmath  isi  scopus
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