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Some new results on bicommutative algebras
Views:4807 Published By:editor
Speaker(s): Zerui Zhang
Time: Aug,11,2021, 14:30PM-15:30PM
Venue: 201 Jinqizhigu Building, No.1 Tangling Road, Nanshan District, Shenzhen

An algebra B is called bicommutative if it satisfies the identities

x(yz) = y(xz) (left commutativity)

(xy)z = (xz)y (right commutativity)

for all x,y,z in B. Wild automorphisms are constructed in two-generated and three-generated free bicommutative algebras. Moreover, for any n \geq 2, a wild automorphism is constructed in the n-generated free associative bicommutative algebra which is not stably tame and cannot be lifted to an automorphism of the n-generated free bicommutative algebra. We also offer fast algorithms for calculating the Gelfand-Kirillov dimension of finitely presented bicommutative algebras.