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We characterize directs sums of twists of symmetric powers of the universal quotient bundle over the Grassmannian of lines. We use a method that could be used for analogue results on any arbitrary variety, and that should give stronger results than using the standard technique of Beilinson's spectral sequence. [ABSTRACT FROM AUTHOR]

In this paper we show that evolution algebras over any given field \Bbbk are universally finite. In other words, given any finite group G, there exist infinitely many regular evolution algebras X such that Aut(X)\cong G. The proof is built upon the construction of a covariant faithful functor from the category of finite simple (non oriented) graphs to the category of (finite dimensional) regular evolution algebras. Finally, we show that any constant finite algebraic affine group scheme \mathbf {G} over \Bbbk is isomorphic to the algebraic affine group scheme of automorphisms of a regular evolution algebra. [ABSTRACT FROM AUTHOR]