We continue our discussion introducing groupoids. All are welcome.
Introduction to Groupoids part 2 Sponsored by the Meyer Fund
Sep. 16, 2014 2pm (MATH 350)
Lie Theory
Megan Ly (CU)
X
The Huneke-Wiegand conjecture, a long-standing open problem in commutative algebra has prompted much recent study. In the category of numerical monoid algebras, Garcia-Sanchez and Leamer provide a reduction theory that equates the Huneeke-Wiegand conjecture to finding certain irreducible arithmetic sequences within numerical monoids. This talk focuses on Leamer monoids, whose elements correspond to arithmetic sequences of a given step size within a fixed numerical monoid, and its factorization theory. In this talk we will provide a description for the first element in the Leamer monoid for numerical monoids generated by two integers using Apery sets. We apply our results to prove the Huneke-Wiegand Conjecture for all numerical monoid algebras of two generators and provide direction for potentially proving the conjecture for numerical monoid algebras with more generators.