Braided symmetric and exterior algebras
By Arkady Berenstein, Sebastian Zwicknagl. 2005
72 citations recorded by the source corpus.
The goal of the paper is to introduce and study symmetric and exterior algebras in certain braided monoidal categories such as the category O for quantum groups. We relate our braided symmetric algebras and braided exterior algebras with their classical counterparts.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/56ff71e0f669063db5b83262a23d8098a035fb1f
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Algebra and Number Theory
In Geometry and Topology
- Sabin Cautis
- Paul Wedrich
- David E. V. Rose
- Hoel Queffelec
- Joel Kamnitzer
- Aaron D. Lauda
- Pedro Vaz
- S. Morrison
In Statistical and Nonlinear Physics
- Sabin Cautis
- Joel Kamnitzer
- S. Morrison
- Pedro Vaz
- Paul Wedrich
- Aaron D. Lauda
- Hoel Queffelec
- David E. V. Rose
Citations in the corpus
- Super $q$-Howe duality and web categories (2015, background): “The projector CL1 is just the black identity strand, the projector CL r 2 is 1 [2] times the red dumbbell as in (10) and CL3= 1 [3]! 1· · ·1”
- Nazarov–Wenzl algebras, coideal subalgebras and categorified skew Howe duality (2013, unknown): “In general it is not obvious how to lift exterior powers to the quantum setting, see [13] for a detailed treatment of this problem.”
- Webs and quantum skew Howe duality (2012, methodology): “ obvious fashion E pz ij= ( z i;j 1 if p= j 1 0 otherwise ; F pz ij= ( z i;j+1 if p= j 0 otherwise ; L pz ij= ( qz ij if p= j z ij otherwise and similarly for the generators of U q(sl n). Recall from [BZ08] that if V is a representation of a quantum group U q(g), then V q (V) always admits a q= 1 s”