Askar Dzhumadil’daev: Dimension formula for Koszul operads

We give recurrence formula for dimensions of Koszul operads. For example, dimensions of multi-linear parts of Lie-admissible operad satisfy the following recurrence relations d_n=∑_i=1^n-1 μ_k B_n-1,k(d₁…d_n-1), where B_n,k are Bell polynomials and μ_k = k! ∑_i=0^k (k–i+1)ⁱ /i !. If p ≥ 5 is prime, then d_p-1 ≡ 1 (mod p), d_p ≡ -1 (mod p), d_p+1 ≡ -1 (mod p), d_p+2 ≡ -6 (mod p), d_p+3 ≡ -56 (mod p), d_p+4 ≡ -725 (mod p).

This video was produced by the Universidade de São Paulo, as part of the LieJor Online Seminar: Algebras, Representations, and Applications.