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Automorphism groups of Cayley evolution algebras
Costoya Ramos, María Cristina; Muñoz, Vicente; Tocino-Sánchez, Alicia; Viruel-Arbaizar, Antonio Ángel (Springer Nature, 2023)In this paper we introduce a new species of evolution algebras that we call Cayley evolution algebras. We show that if a field k contains sufficiently many elements (for example if k is infinite) then every finite group ... -
Finite sets containing zero are mapping degree sets
Costoya Ramos, María Cristina; Muñoz, Vicente; Viruel-Arbaizar, Antonio Ángel (Elsevier, 2024)In this paper we solve in the positive the question of whether any finite set of integers, containing 0, is the mapping degree set between two oriented closed connected manifolds of the same dimension. We extend this ... -
Realisability problems in Algebraic Topology
Mendez Martinez, David (UMA Editorial, 2020-02-24)Realisability problems in Algebraic Topology are very easy to state and extremely hard to solve. Three classic examples of this are: the realisability of cohomology algebras, proposed by N. E. Steenrod in the 1960s, which ... -
Regular evolution algebras are universally finite.
Costoya Ramos, María Cristina; Ligouras, Panagiote; Tocino-Sánchez, Alicia; Viruel-Arbaizar, Antonio Ángel (AMS, 2021-12-14)In this paper we show that evolution algebras over any given field k are universally finite. In other words, given any finite group G, there exist infinitely many regular evolution algebras X such that Aut(X) ∼= G. The ...