A pairing between graphs and trees Export

@misc{citeulike:106606, abstract = {We develop a canonical pairing between trees and graphs, which passes to their quotients by Jacobi identities. This pairing is an effective and simple tool for understanding the Lie and Poisson operads, providing canonical duals. In the course of showing that this pairing is perfect we reprove some standard facts about the modules Lie(n), establishing standard bases as well as giving a new means to reduce to those bases. We then move on to develop product, coproduct and operad structures. We give a brief account here to be built on in a number of different directions in future work.}, archivePrefix = {arXiv}, author = {Sinha, Dev P.}, citeulike-article-id = {106606}, citeulike-linkout-0 = {http://arxiv.org/abs/math.QA/0502547}, citeulike-linkout-1 = {http://arxiv.org/pdf/math.QA/0502547}, eprint = {math.QA/0502547}, keywords = {algebra, category-theory, graphs, mathematics}, month = {February}, posted-at = {2006-06-21 02:19:35}, priority = {2}, title = {A pairing between graphs and trees}, url = {http://arxiv.org/abs/math.QA/0502547}, year = {2005} }

TY - ELEC ID - citeulike:106606 L3 - citeulike-article-id:106606 N2 - We develop a canonical pairing between trees and graphs, which passes to their quotients by Jacobi identities. This pairing is an effective and simple tool for understanding the Lie and Poisson operads, providing canonical duals. In the course of showing that this pairing is perfect we reprove some standard facts about the modules Lie(n), establishing standard bases as well as giving a new means to reduce to those bases. We then move on to develop product, coproduct and operad structures. We give a brief account here to be built on in a number of different directions in future work. TI - A pairing between graphs and trees KW - algebra KW - category-theory KW - graphs KW - mathematics AU - Sinha, Dev PY - 2005/02/25/ UR - http://arxiv.org/abs/math.QA/0502547 ER -