Testing isomorphism of complex and real Lie algebras

Abstract

In this paper, we give algorithms for determining the existence of isomorphism between two finite-dimensional Lie algebras and compute such an isomorphism in the affirrmative case. We also provide algorithms for determining algebraic relations of parameters in order to decide whether two parameterized Lie algebras are isomorphic. All of the considered Lie algebras are considred over a field F, where F = C or F = R. Several illustrative examples are given to show the applicability and the effectiveness of the proposed algorithms.

Classification of 7-dimensional solvable Lie algebras having 5-dimensional nilradicals

“…This testing isomorphism procedure is specified by algorithms that are run by Maple software with supports of a hyper-computer. Details of these algorithms can be found in [24]. We also note that these algorithms in [24] are valid over fields of characteristic not only 0 but also prime.…”

“…Details of these algorithms can be found in [24]. We also note that these algorithms in [24] are valid over fields of characteristic not only 0 but also prime. In this paper, we simply use them over F. Remark 2.1.…”

“…a, 1 + a, 2 + a, 0), (0, b, b, b, 1) b = 0; L ab =0 4 should be added to Wang et al [41, Theorem 3]L a , 1, 2, 3, a), (0, 0, 0, 0, 1) + E 12 L 6 (0, 1, 1, 1, 0), (1, 0, 1, 2, 1) + E 15 L a a, 1 + a, 2 + a, 1), (0, 1, 1, 1, 0) + E 15 L aδ 0, 1, 1, 1, a), (0, 0, 0, 0, 1) + δE24 Over C:δ = 1 L 9 (0, 1, 1,1, 1), (1, 0, 1, 2, 0) + E 25 Should be added to Wang et al [41, Theorem 3] L a a, 1 + a, 2 + a, a), (0, 1, 1, 1, 1) + E 25 Should be added to Wang et al [41, Theorem 3] L 11 (0, 1, 1, 1, 1), (1, 0, 1, 2, 2) + E 54 L a a, 1+ a, 2+ a, 2+ a), (0, 1, 1, 1, 1)+ E 54…”