Publications Influence

Share This Author

A DG-extension of symmetric functions arising from higher representation theory

- Andrea Appel, Ilknur Egilmez, Matthew Hogancamp, Aaron D. Lauda
- Mathematics
- 3 April 2017

We investigate analogs of symmetric functions arising from an extension of the nilHecke algebra defined by Naisse and Vaz. These extended symmetric functions form a subalgebra of the polynomial ring… Expand

An explicit isomorphism between quantum and classical sl(n)

- Andrea Appel, S. Gautam
- Mathematics
- 10 December 2017

Let g be a complex, semisimple Lie algebra. Drinfeld showed that the quantum group associated to g is isomorphic as an algebra to the trivial deformation of the universal enveloping algebra of g. In… Expand

Quasi-Coxeter categories and a relative Etingof-Kazhdan quantization functor

- Andrea Appel, V. Toledano-Laredo
- Mathematics
- 30 December 2012

Let g be a symmetrizable Kac-Moody algebra and U_h(g) its quantized enveloping algebra. The quantum Weyl group operators of U_h(g) and the universal R-matrices of its Levi subalgebras endow U_h(g)… Expand

Uniqueness of Coxeter structures on Kac–Moody algebras

- Andrea Appel, V. Toledano-Laredo
- MathematicsAdvances in Mathematics
- 8 August 2015

Monodromy of the Casimir connection of a symmetrisable Kac-Moody algebra

- Andrea Appel, V. Toledano-Laredo
- Mathematics
- 9 December 2015

Let g be a symmetrisable Kac-Moody algebra and V an integrable g-module in category O. We show that the monodromy of the (normally ordered) rational Casimir connection on V can be made equivariant… Expand

Universal K-matrices for quantum Kac-Moody algebras

- Andrea Appel, Bart Vlaar
- MathematicsRepresentation Theory of the American…
- 17 July 2020

We introduce the notion of a cylindrical bialgebra, which is a quasitriangular bialgebra
H
H
endowed with a universal K-matrix, i.e., a universal solution of a generalized reflection… Expand

Coxeter categories and quantum groups

- Andrea Appel, V. Toledano-Laredo
- MathematicsSelecta Mathematica
- 31 October 2016

We define the notion of braided Coxeter category, which is informally a monoidal category carrying compatible, commuting actions of a generalised braid group \(B_W\) and Artin’s braid groups \(B_n\)… Expand

A 2-categorical extension of Etingof–Kazhdan quantisation

- Andrea Appel, V. Toledano Laredo
- Mathematics
- 31 October 2016

Let $$\mathsf {k}$$k be a field of characteristic zero. Etingof and Kazhdan (Sel. Math. (N.S.) 2:1–41, 1996) construct a quantisation $$U_\hbar \mathfrak b$$Uħb of any Lie bialgebra $$\mathfrak b$$b… Expand

Quantization of continuum Kac–Moody algebras

- Andrea Appel, Francesco Sala
- Mathematics
- 4 March 2019

Continuum Kac-Moody algebras have been recently introduced by the authors and O. Schiffmann. These are Lie algebras governed by a continuum root system, which can be realized as uncountable colimits… Expand

Monodromy theorems in the affine setting

- Andrea Appel
- Education
- 2013

of Dissertation Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in Mathematics in the College of Science of Northeastern University

...

1

2

...