Lectures on Quantum Groups

By Pavel Etingof, O. Schiffmann. 2001

691 citations recorded by the source corpus.

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Citations in the corpus

The Multiple Zeta Value Algebra and the Stable Derivation Algebra (2000, background): “ surjectivity of ΨDRimplies Corollary 4.3.1. (i) dimQNZw6 dimQ Dw. (ii) More precisely, dimQNZ6m w 6 dimQ F mD∗ w = dimQ (Dw/ m+1Dw). M. Kaneko informed me that Corollary 4.3.1(i) is also appeared in [4], which was deduced from the action of the stable derivation algebra on a certain torsor. Proposi”
Quantum Groups and Quantum Cohomology (2012, background): “h is equivalent to the equation rr 12;r 13sr r 12;r 23sr r 13;r 23s0; r ij r ij a i a j : (4.23) This is know as the classical Yang-Baxter equation with spectral parameter, see e.g. Section 6.3 in [33]. For brevity, we call r and not r, which contains the exact same information, the classical R-mat”
An Introduction to Lie Groups and Lie Algebras (2008, background): “A good introduction to quantum groups can be found in the books of Jantzen [25] or Kassel [28].”
Moduli of representations of quivers (2008, background): “Its enveloping algebra U(g) admits a quantum deformation, the quantized enveloping algebra Uq(g) [32, 45].”
Strongly multiplicity free modules for Lie algebras and quantum groups (2006, background): “Recall [ Ja , 5.3, p.71] that for any finite dimensional Uq(g)-module W and 2 EndC(W), the quantum trace trq,W( ) = trW(K ) is a Uq(g)-module homomorphism to the trivial Uq(g)-module.”
A new approach to Kazhdan-Lusztig theory of type ${\bf B}$ via quantum symmetric pairs (2013, unknown): “(The Tαi here is consistent with Tαi in [Jan], and it is T ′′ i,+ in [Lu2]).”
Deformation Quantization: Genesis, Developments and Metamorphoses (2002, background): “ebra. By this we mean an associative, Lie or Hopf algebra, or a bialgebra [an associative algebra A where one has in addition a coproduct ∆: A −→ A⊗A and the obvious compatibility relations, see e.g. [ES] for a precise deﬁnition]. Whenever needed we assume it is also a topological algebra, i.e., end”
Parabolic Presentations of the Yangian (2004, unknown): “To define the Yangian Yn = Y( gln) we use the RTT formalism; see [ ES , ch. 11] or [FRT].”
Lectures on algebraic categorification (2010, background): “ng: Lemma 11.3. Formulae (11.1) and (11.2) deﬁne on both Vnand Vˆnthe structure of a simple Uv(sl2)-module of dimension n+1. For n= 1 the module V1 is called the natural Uv(sl2)-module. Theorem 11.4 ([Ja3]). (a) For every n∈ N0 there is a unique simple Uv(sl2)- module of dimension n+ 1, namely Vn, o”
A relation between a conjecture of Kac and the structure of the Hall algebra (2001, background): “We refer the reader to the excellent books [5,6] or [11].”
Etingof–Kazhdan quantization of Lie superbialgebras (2004, methodology): “For the rest of this paper when considering Lie superalgebras of type A-G we will assume that these Lie superalgebras are defined by the generators and relations given in Theorem 5.”
The brundan-kazhdan-lusztig conjecture for general linear lie superalgebras (2012, methodology): “In what follows we shall apply results from [Lu2] and [Jan].”