8 papers
Quantum groups of Borcherds-Cartan type and Khovanov-Lauda-Rouquier algebras
Seok-Jin Kang, Young Rock Kim, Bolun Tong
We categorify a class of quantum groups associated with quivers, possibly with loops, by constructing the corresponding Khovanov-Lauda-Rouquier algebras (KLR) algebras . We prov…
Quiver Hecke algebras for Borcherds-Cartan datum II
Bolun Tong, Wan Wu
We give the crystal structure of the Grothendieck group of irreducible modules over the quiver Hecke algebra constructed in \cite{TW2023}. This leads to the categorifi…
Categorification of quantum Borcherds-Bozec algebras
Seok-Jin Kang, Young Rock Kim, Bolun Tong
We categorify the quantum Borcherds-Bozec algebras by constructing their associated Khovanov-Lauda-Rouquier algebras.
Quiver Hecke algebras for Borcherds-Cartan datum
Bolun Tong, Wan Wu
We introduce a family of quiver Hecke algebras which give a categorification of quantum Borcherds algebra associated to an arbitrary Borcherds-Cartan datum.
Braid group actions of quantum Borcherds-Bozec algebras
Zhaobing Fan, Bolun Tong
In this paper, we construct the Lusztig symmetries for quantum Borcherds-Bozec algebra and its weight module , on which the generators with real…
Global bases for quantum Borcherds-Bozec algebras
Zhaobing Fan, Seok-Jin Kang, Young Rock Kim +1
We provide a construction of global bases for quantum Borcherds-Bozec algebras and their integrable highest weight representations.
Abstract crystals for quantum Borcherds-Bozec algebras
Zhaobing Fan, Seok-Jin Kang, Young Rock Kim +1
In this paper, we develop the theory of abstract crystals for quantum Borcherds-Bozec algebras. Our construction is different from the one given by Bozec. We further prove the crys…
Classical limit of quantum Borcherds-Bozec algebras
Zhaobing Fan, Seok-Jin Kang, Young-Rock Kim +1
Let be a Borcherds-Bozec algebra, be its universal enveloping algebra and be the corresponding quantum Borcherds-Bozec algebr…