Admissible Skein Modules

In this paper we introduce the notion of admissible skein modules associated to an ideal in a pivotal category. We explain how these modules are generalizations of the Kauffman skein algebra and how they relate to renormalized quantum invariants coming from non-semisimple categories.

[1]  Nathan Geer,et al.  Non compact (2+1)-TQFTs from non-semisimple spherical categories , 2023, 2302.04509.

[2]  B. Bartlett.  Three-dimensional TQFTs via string-nets and two-dimensional surgery , 2022, 2206.13262.

[3]  Cristina Ana-Maria Anghel,et al.  Relative (pre)-modular categories from special linear Lie superalgebras , 2020, 2010.13759.

[4]  Thorsten Heidersdorf,et al.  Generalized negligible morphisms and their tensor ideals , 2019, Selecta Mathematica.

[5]  S. Gunningham,et al.  The finiteness conjecture for skein modules , 2019, Inventiones mathematicae.

[6]  Thang T. Q. Lê,et al.  Stated skein algebras of surfaces , 2019, Journal of the European Mathematical Society.

[7]  V. Turaev,et al.  Kuperberg and Turaev–Viro invariants in unimodular categories , 2018, 1809.07991.

[8]  Thang T. Q. Lê,et al.  Unicity for representations of the Kauffman bracket skein algebra , 2017, Inventiones mathematicae.

[9]  Nathan Geer,et al.  The trace on projective representations of quantum groups , 2016, 1610.09129.

[10]  David Ben-Zvi,et al.  Integrating quantum groups over surfaces , 2015, Journal of Topology.

[11]  E. Witten,et al.  Branes and Supergroups , 2014, 1410.1175.

[12]  Nathan Geer,et al.  Non semi-simple TQFTs, Reidemeister torsion and Kashaev's invariants , 2014, 1404.7289.

[13]  D. Thurston.  Positive basis for surface skein algebras , 2013, Proceedings of the National Academy of Sciences.

[14]  Nathan Geer,et al.  Quantum invariants of 3‐manifolds via link surgery presentations and non‐semi‐simple categories , 2012, 1202.3553.

[15]  J. Kujawa.  The generalized Kac-Wakimoto conjecture and support varieties for the Lie superalgebra osp(m|2n) , 2011, 1112.3384.

[16]  Nathan Geer,et al.  Ambidextrous objects and trace functions for nonsemisimple categories , 2011, 1106.4477.

[17]  Nathan Geer,et al.  Traces on ideals in pivotal categories , 2011, 1103.1660.

[18]  F. Bonahon,et al.  Quantum traces for representations of surface groups in SL2(ℂ) , 2010, 1003.5250.

[19]  Nathan Geer,et al.  Generalized trace and modified dimension functions on ribbon categories , 2010, 1001.0985.

[20]  V. Turaev,et al.  Modified quantum dimensions and re-normalized link invariants , 2007, Compositio Mathematica.

[21]  A. Sikora.  SKEIN MODULES AND TQFT , 2000 .

[22]  J. Przytycki.  Fundamentals of Kauffman bracket skein modules , 1998, math/9809113.

[23]  V. Turaev.  Quantum Invariants of Knots and 3-Manifolds , 1994, hep-th/9409028.

[24]  Bruce W. Westbury,et al.  Spherical Categories , 1993, hep-th/9310164.

[25]  V. Serganova.  On the Superdimension of an Irreducible Representation of a Basic Classical Lie Superalgebra , 2011 .

[26]  D. Bullock.  Rings of SL2(C)-characters and the Kauman bracket skein module , 1997 .

[27]  G. Maltsiniotis.  Traces dans les catégories monoïdales, dualité et catégories monoïdales fibrées , 1995 .

[28]  V. Turaev.  Skein quantization of Poisson algebras of loops on surfaces , 1991 .