RT Journal Article
T1 Hopf Algebras and Associative Representations of Two-Dimensional Evolution .
A1 Cabrera-Casado, Yolanda
A1 Cardoso Gonçalves, Maria Inez
A1 Gonçalves, Daniel
A1 Martín-Barquero, Dolores
A1 Martín-González, Cándido
A1 Ruiz Campos, Iván
K1 Hopf, Algebras de
K1 Topología algebraica
K1 Variedades algebraicas
K1 Automorfismos
AB In this paper, we establish a connection between evolution algebrasof dimension two and Hopf algebras, via the algebraic group of automorphismsof an evolution algebra. Initially, we describe the Hopf algebra associated withthe automorphism group of a 2-dimensional evolution algebra. Subsequently,for a 2-dimensional evolution algebra A over a field K, we detail the relationbetween the algebra associated with the (tight) universal associative andcommutative representation of A, referred to as the (tight) p-algebra, and thecorresponding Hopf algebra, H , representing the affine group scheme Aut(A).Our analysis involves the computation of the (tight) p−algebra associatedwith any 2-dimensional evolution algebra, whenever it exists. We find thatAut(A) = 1 if and only if there is no faithful associative and commutativerepresentation for A. Moreover, there is a faithful associative and commutativerepresentation for A if and only if H ̸∼= K and char(K) ̸= 2, or H ̸∼= K(ϵ) (thedual numbers algebra) and H ̸∼= K in case of char(K) = 2. Furthermore, if Ais perfect and has a faithful tight p-algebra, then this p-algebra is isomorphic toH (as algebras). Finally, we derive implications for arbitrary finite-dimensionalevolution algebras
PB Springer Nature
YR 2024
FD 2024-12-26
LK https://hdl.handle.net/10630/40029
UL https://hdl.handle.net/10630/40029
LA eng
NO Cabrera Casado, Y., Cardoso Gonçalves, M.I., Gonçalves, D. et al. Hopf Algebras and Associative Representations of Two-Dimensional Evolution Algebras. Bull Braz Math Soc, New Series 56, 8 (2025). https://doi.org/10.1007/s00574-024-00433-4
NO https://openpolicyfinder.jisc.ac.uk/id/publication/7875
DS RIUMA. Repositorio Institucional de la Universidad de Málaga
RD 21 ene 2026