Geodesic
Automorphic equivalence of the representations of Lie algebras
Algebra and discrete mathematics, Tome 15 (2013) no. 1, pp. 96-126.

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In this paper we research the algebraic geometry of the representations of Lie algebras over fixed field $k$. We assume that this field is infinite and $char\left(k\right) =0$. We consider the representations of Lie algebras as $2$-sorted universal algebras. The representations of groups were considered by similar approach: as $2$-sorted universal algebras — in [3] and [2]. The basic notions of the algebraic geometry of representations of Lie algebras we define similar to the basic notions of the algebraic geometry of representations of groups (see [2]). We prove that if a field $k$ has not nontrivial automorphisms then automorphic equivalence of representations of Lie algebras coincide with geometric equivalence. This result is similar to the result of [4], which was achieved for representations of groups. But we achieve our result by another method: by consideration of $1$-sorted objects. We suppose that our method can be more perspective in the further researches.
Keywords: universal algebraic geometry, representations of Lie algebras, automorphic equivalence. 
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I. Shestakov; A. Tsurkov. Automorphic equivalence of the representations of Lie algebras. Algebra and discrete mathematics, Tome 15 (2013) no. 1, pp. 96-126. http://geodesic.mathdoc.fr/item/ADM_2013_15_1_a8/

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