Access the full text.
Sign up today, get DeepDyve free for 14 days.
(1989)
and W
Sven Raum, Moritz Weber (2013)
The Full Classification of Orthogonal Easy Quantum GroupsCommunications in Mathematical Physics, 341
Amaury Freslon, Moritz Weber (2013)
On the representation theory of partition (easy) quantum groupsarXiv: Quantum Algebra
K. Commer, Amaury Freslon, M. Yamashita (2013)
CCAP for Universal Discrete Quantum GroupsCommunications in Mathematical Physics, 331
J. Bichon, An Rijdt, S. Vaes (2005)
Ergodic Coactions with Large Multiplicity and Monoidal Equivalence of Quantum GroupsCommunications in Mathematical Physics, 262
Teodor Banica (1998)
Theorie des representations du groupe quantique compact libre O(n)arXiv: Quantum Algebra
T. Banica, Adam Skalski (2010)
Quantum isometry groups of duals of free powers of cyclic groupsarXiv: Operator Algebras
S. Woronowicz (1987)
Compact matrix pseudogroupsCommunications in Mathematical Physics, 111
L. Pittau (2014)
The free wreath product of a discrete group by a quantum automorphism grouparXiv: Quantum Algebra
Paul Martin (1994)
TEMPERLEY-LIEB ALGEBRAS FOR NON-PLANAR STATISTICAL MECHANICS — THE PARTITION ALGEBRA CONSTRUCTIONJournal of Knot Theory and Its Ramifications, 03
Franccois Lemeux (2013)
The fusion rules of some free wreath product quantum groups and applicationsarXiv: Operator Algebras
T. Banica, R. Speicher (2008)
Liberation of orthogonal Lie groupsAdvances in Mathematics, 222
Matthew Bloss (2003)
G-colored partition algebras as centralizer algebras of wreath productsJournal of Algebra, 265
T. Banica, Roland Vergnioux (2008)
Fusion rules for quantum reflection groupsJournal of Noncommutative Geometry, 3
A. Daele, Shuzhou Wang (1996)
UNIVERSAL QUANTUM GROUPSInternational Journal of Mathematics, 07
K. Tanabe (1997)
On the centralizer algebra of the unitary reflection group G(m,p,n)Nagoya Mathematical Journal, 148
Michael Brannan (2012)
Reduced operator algebras of trace-preserving quantum automorphism groupsDocumenta Mathematica
T. Banica, Adam Skalski (2010)
Two-parameter families of quantum symmetry groupsarXiv: Operator Algebras
The Potts model and the symmetric group
T. Banica (2007)
A note on free quantum groupsarXiv: Quantum Algebra
P. Glockner, W. Waldenfels (1989)
The relations of the non-commutative coefficient algebra of the unitary group, 4
T. Banica (1998)
Representations of compact quantum groups and subfactorsJournal für die reine und angewandte Mathematik (Crelles Journal), 1999
J. Tarragó, Moritz Weber (2015)
The classification of tensor categories of two-colored noncrossing partitionsJ. Comb. Theory, Ser. A, 154
Teodor Banica (1997)
Le Groupe Quantique Compact Libre U(n)Communications in Mathematical Physics, 190
Amaury Freslon, Moritz Weber (2013)
On the representation theory of easy quantum groupsarXiv: Quantum Algebra
Shuzhou Wang (1998)
Quantum Symmetry Groups of Finite SpacesCommunications in Mathematical Physics, 195
T. Banica (1998)
Symmetries of a generic coactionMathematische Annalen, 314
M. Parvathi, Joseph Kennedy (2004)
G-Vertex Colored Partition Algebras as Centralizer Algebras of Direct ProductsCommunications in Algebra, 32
G. Lehrer, R. Zhang (2012)
The Brauer Category and Invariant TheoryarXiv: Group Theory
F Knop (2006)
A construction of semisimple tensor categoriesC. R. Acad. Sci. Paris Sér. I Math., 343
T Banica (1999)
Fusion rules for compact quantum groupsExposition. Math., 17
François Lemeux (2015)
Haagerup approximation property for quantum reflection groups, 143
Franccois Lemeux (2013)
Haagerup property for quantum reflection groupsarXiv: Operator Algebras
A. Nica, R. Speicher (2006)
Lectures on the Combinatorics of Free Probability
Postfach 151159, 66041 Saarbrücken, Germany E-mail address: freslon@math.uni-sb
M. Kosuda (2008)
CHARACTERIZATION FOR THE MODULAR PARTY ALGEBRAJournal of Knot Theory and Its Ramifications, 17
(2007)
La catégorie des représentations du groupe symétrique St, lorsque t n’est pas un entier naturel, Algebraic groups and homogeneous spaces
Amaury Freslon (2012)
Examples of weakly amenable discrete quantum groupsarXiv: Operator Algebras
T. Banica, S. Belinschi, M. Capitaine, Benoît Collins (2007)
Free Bessel LawsCanadian Journal of Mathematics, 63
J. Bichon (2001)
Free Wreath Product by the Quantum Permutation GroupAlgebras and Representation Theory, 7
Shuzhou Wang (1995)
Free products of compact quantum groupsCommunications in Mathematical Physics, 167
Sven Raum (2010)
Isomorphisms and Fusion Rules of Orthogonal Free Quantum Groups and their ComplexificationsarXiv: Operator Algebras
Franccois Lemeux, Pierre Tarrago (2014)
Free wreath product quantum groups : the monoidal category, approximation properties and free probabilityarXiv: Quantum Algebra
Amaury Freslon (2013)
Fusion (semi)rings arising from quantum groupsarXiv: Quantum Algebra
Matthew Daws, Pierre Fima, Adam Skalski, Stuart White (2013)
The Haagerup property for locally compact quantum groupsarXiv: Operator Algebras
F. Knop (2006)
A construction of semisimple tensor categoriesComptes Rendus Mathematique, 343
S. Woronowicz (1988)
Tannaka-Krein duality for compact matrix pseudogroups. TwistedSU(N) groupsInventiones mathematicae, 93
S. Vaes, Roland Vergnioux (2005)
The boundary of universal discrete quantum groups, exactness, and factorialityDuke Mathematical Journal, 140
M. Mori (2011)
On representation categories of wreath products in non-integral rankAdvances in Mathematics, 231
F. Knop (2006)
Tensor envelopes of regular categoriesAdvances in Mathematics, 214
C. Mrozinski (2013)
Quantum automorphism groups and SO(3)-deformationsJournal of Pure and Applied Algebra, 219
R. Brauer (1937)
On Algebras Which are Connected with the Semisimple Continuous GroupsAnnals of Mathematics, 38
S. Neshveyev, L. Tuset (2014)
Compact Quantum Groups and Their Representation Categories
We give a general definition of classical and quantum groups whose representation theory is “determined by partitions” and study their structure. This encompasses many examples of classical groups for which Schur-Weyl duality is described with diagram algebras as well as generalizations of P. Deligne's interpolated categories of representations. Our setting is inspired by many previous works on easy quantum groups and appears to be well suited to the study of free fusion semirings. We classify free fusion semirings and prove that they can always be realized through our construction, thus solving several open questions. This suggests a general decomposition result for free quantum groups which in turn gives information on the compact groups whose Schur-Weyl duality is implemented by partitions. The paper also contains an appendix by A. Chirvasitu proving simplicity results for the reduced C*-algebras of some free quantum groups.
Transformation Groups – Springer Journals
Published: Oct 26, 2016
Read and print from thousands of top scholarly journals.
Already have an account? Log in
Bookmark this article. You can see your Bookmarks on your DeepDyve Library.
To save an article, log in first, or sign up for a DeepDyve account if you don’t already have one.
Copy and paste the desired citation format or use the link below to download a file formatted for EndNote
Access the full text.
Sign up today, get DeepDyve free for 14 days.
All DeepDyve websites use cookies to improve your online experience. They were placed on your computer when you launched this website. You can change your cookie settings through your browser.