Algebraic structures on modules of diagrams

作者：Vogel Pierre^*

来源：Journal of Pure and Applied Algebra, 2011, 215(6): 1292-1339.

DOI：10.1016/j.jpaa.2010.08.013

There exists a graded algebra A acting in a natural way on many modules of 3-valent diagrams. Every simple Lie superalgebra with a nonsingular invariant bilinear form induces a character on A. The classical and exceptional Lie algebras and the Lie superalgebra D(2, 1, alpha) produce eight distinct characters on A and eight distinct families of weight functions on chord diagrams. As a consequence we prove that weight functions coming from semisimple Lie superalgebras do not detect every element in the module A of chord diagrams. A precise description of A is conjectured.

• 出版日期2011-6