A categorification of quantum sl(2) Export

@article{citeulike:3891711, abstract = {We categorify Lusztig's version of the quantized enveloping algebra for sl(2). Using a graphical calculus a 2-category is constructed whose split Grothendieck ring is isomorphic to Lusztig's algebra. The indecomposable morphisms of this 2-category lift Lusztig's canonical basis, and the Homs between 1-morphisms are graded lifts of a semilinear form defined on quantum sl(2). Graded lifts of various homomorphisms and antihomomorphisms of Lusztig's algebra arise naturally in the context of our graphical calculus. Using iterated flag varieties, a representation of the 2-category is constructed for each positive integer N. This representation categorifies the irreducible (N+1)-dimensional representation of quantum sl(2).}, archivePrefix = {arXiv}, author = {Lauda, Aaron D.}, citeulike-article-id = {3891711}, citeulike-linkout-0 = {http://arxiv.org/abs/0803.3652}, citeulike-linkout-1 = {http://arxiv.org/pdf/0803.3652}, day = {13}, eprint = {0803.3652}, keywords = {categorification, quantum\_groups}, month = {Aug}, posted-at = {2009-01-16 12:48:02}, priority = {0}, title = {A categorification of quantum sl(2)}, url = {http://arxiv.org/abs/0803.3652}, year = {2008} }

TY - JOUR ID - citeulike:3891711 L3 - citeulike-article-id:3891711 N2 - We categorify Lusztig's version of the quantized enveloping algebra for sl(2). Using a graphical calculus a 2-category is constructed whose split Grothendieck ring is isomorphic to Lusztig's algebra. The indecomposable morphisms of this 2-category lift Lusztig's canonical basis, and the Homs between 1-morphisms are graded lifts of a semilinear form defined on quantum sl(2). Graded lifts of various homomorphisms and antihomomorphisms of Lusztig's algebra arise naturally in the context of our graphical calculus. Using iterated flag varieties, a representation of the 2-category is constructed for each positive integer N. This representation categorifies the irreducible (N+1)-dimensional representation of quantum sl(2). TI - A categorification of quantum sl(2) KW - categorification KW - quantum_groups AU - Lauda, Aaron PY - 2008/Aug/13/ UR - http://arxiv.org/abs/0803.3652 ER -