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26 results on '"Gan, Wee Liang"'

7. Quantization of the Lie Bialgebra of String Topology

Author

Chen, Xiaojun, Eshmatov, Farkhod, and Gan, Wee Liang

Subjects
Physics, Classical and Quantum Gravitation, Relativity Theory, Statistical Physics, Dynamical Systems and Complexity, Quantum Physics, Theoretical, Mathematical and Computational Physics
Abstract

Let M be a smooth, simply-connected, closed oriented manifold, and LM the free loop space of M. Using a Poincaré duality model for M, we show that the reduced equivariant homology of LM has the structure of a Lie bialgebra, and we construct a Hopf algebra which quantizes the Lie bialgebra.

Published
2011

12. Problems

Author

Cipra, Barry, Fukuta, Jiro, Morris, Howard, Carter, Larry, Duncan, John, Wagon, Stan, Trautman, Dave, Schaumberger, Norman, Klamkin, Murray S., Bracken, Paul, Flanigan, F. J., Gan, Wee Liang, Doster, David, Locke, Stephen C., Jeremiason, David, Weinstein, Elliott A., and Holzsager, Richard

Published
1994
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13. Problems

Author

Klamkin, Murray S., Gan, Wee Liang, Doster, David, Fukuta, Jiro, Weinstein, Elliott A., Li, Wenbo V., Goffinet, Daniel, Goffinet, Patrick, Friedlander, Richard, Wagon, Stan, Bloom, D. M., Gauchman, Hillel, Rosenholtz, Ira, Martin, Reiner, Demir, Huseyin, Laugwitz, Detlef, Callan, David, and Barrett, David Jonathan

Published
1993
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14. Adjoint functors on the representation category of $\mathscr{OI}$

Author

Gan, Wee Liang and Li, Liping

Subjects
Rings and Algebras (math.RA), Mathematics::K-Theory and Homology, Mathematics::Category Theory, FOS: Mathematics, Mathematics - Rings and Algebras, Representation Theory (math.RT), Mathematics - Representation Theory
Abstract

In this paper we study adjunction relations between some natural functors on the representation category of the category of finite linearly ordered sets and order-preserving injections. We also prove that the Nakayama functor induces an equivalence from the Serre quotient of the category of finitely generated modules by the category of finitely generated torsion modules to the category of finite dimensional modules.

Published
2021

20. A long exact sequence for homology of FI-modules

Author

Gan, Wee Liang

Subjects
Mathematics::K-Theory and Homology, FOS: Mathematics, Representation Theory (math.RT), Mathematics::Symplectic Geometry, Mathematics::Algebraic Topology, Mathematics - Representation Theory
Abstract

We construct a long exact sequence involving the homology of an FI-module. Using the long exact sequence, we give two methods to bound the Castelnuovo-Mumford regularity of an FI-module which is generated and related in finite degree. We also prove that for an FI-module which is generated and related in finite degree, if it has a nonzero higher homology, then its homological degrees are strictly increasing (starting from the first homological degree)., Minor corrections

Published
2016

21. Harish-Chandra homomorphisms and symplectic reflection algebras for wreath-products

Author

Etingof, Pavel, Gan, Wee Liang, Ginzburg, Victor, and Oblomkov, Alexei

Subjects
Mathematics::Rings and Algebras, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Representation Theory (math.RT), Mathematics::Representation Theory, Mathematics - Representation Theory
Abstract

The main result of the paper is a natural construction of the spherical subalgebra in a symplectic reflection algebra associated with a wreath-product in terms of quantum hamiltonian reduction of an algebra of differential operators on a representation space of an extended Dynkin quiver. The existence of such a construction has been conjectured in [EG]. We also present a new approach to reflection functors and shift functors for generalized preprojective algebras and symplectic reflection algebras associated with wreath-products., Introduction expanded

Published
2005

22. On central stability.

Author

Gan, Wee Liang and Li, Liping

Subjects
SYMMETRY groups, STABILITY theory, MATHEMATICAL sequences, REPRESENTATIONS of algebras, MODULES (Algebra), TOPOLOGICAL degree
Abstract

The notion of central stability was first formulated for sequences of representations of the symmetric groups by Putman. A categorical reformulation was subsequently given by Church, Ellenberg, Farb, and Nagpal using the notion of FI-modules, where FI is the category of finite sets and injective maps. We extend the notion of central stability from FI to a wide class of categories, and prove that a module is presented in finite degrees if and only if it is centrally stable. We also introduce the notion of [ABSTRACT FROM AUTHOR]

Published
2017
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23. Hamiltonian reduction and Maurer-Cartan equations

Author

Gan, Wee Liang and Ginzburg, Victor

Subjects
Mathematics - Algebraic Geometry, Mathematics - Symplectic Geometry, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Symplectic Geometry (math.SG), Algebraic Geometry (math.AG), Mathematics::Symplectic Geometry
Abstract

We show that solving the Maurer-Cartan equations is, essentially, the same thing as performing the Hamiltonian reduction construction. In particular, any differential graded Lie algebra equipped with an even nondegenerate invariant bilinear form gives rise to modular stacks with symplectic structures., 9 pp., expanded version: more details and comments added

Published
2003

24. Quantization of Slodowy slices

Author

Gan, Wee Liang and Ginzburg, Victor

Subjects
Mathematics - Algebraic Geometry, Mathematics - Quantum Algebra, FOS: Mathematics, Quantum Algebra (math.QA), Representation Theory (math.RT), Algebraic Geometry (math.AG), Mathematics - Representation Theory
Abstract

We give a direct proof of (a slight generalization of) the recent result of A. Premet related to generalized Gelfand-Graev representations and of an equivalence due to Skryabin., An appendix is added providing some details concerning section 3.1

Published
2001

25. Coinduction functor in representation stability theory.

Author

Gan, Wee Liang and Li, Liping

Subjects
*COINDUCTION (Mathematics), *FUNCTOR theory, *REPRESENTATION theory, *STABILITY theory, *HOMOLOGY theory
Abstract

We study the coinduction functor on the category of FI-modules and its variants. Using the coinduction functor, we give new proofs of (generalizations of) various results on homological properties of FI-modules. We also prove that any finitely generated projective VI-module over a field of characteristic 0 is injective. [ABSTRACT FROM AUTHOR]

Published
2015
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26. Quantization of Slodowy slices.

Author

Gan, Wee Liang and Ginzburg, Victor

Subjects
*GEOMETRIC quantization, *MATHEMATICAL proofs, *NILPOTENT groups, *MATHEMATICAL analysis, *SCATTERING (Mathematics)
Abstract

We give a direct proof of (a slight generalization of) the recent result of Premet (1999) related to generalized Gelfand-Graev representations and of an equivalence due to Skryabin (2000). [ABSTRACT FROM AUTHOR]

Published
2002
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