Solvable Lie algebras with maximal dimension of complementary space to nilradical

On solvable Lie and Leibniz superalgebras with maximal codimension of nilradical

“…solvable extension by means of (super)derivations of nilradical, for more details it can be consulted [9]. Considering now L n,m as a Lie algebra, the results of [17] allow us to assert that there is a unique solvable Lie algebra with maximal codimension of nilradical, i.e. maximal dimension of the complementary space to nilradical.…”

“…Moreover this maximal codimension is equal to the number of generators of the nilradical, 3 in our case. It can be easily seen that this unique solvable Lie algebra described in [17] is isomorphic to SL n,m , considered the latter as a Lie algebra. Indeed, following to Theorem 3.2 [17] we have a solvable Lie algebra…”

“…It can be easily seen that this unique solvable Lie algebra described in [17] is isomorphic to SL n,m , considered the latter as a Lie algebra. Indeed, following to Theorem 3.2 [17] we have a solvable Lie algebra…”

“…as a Lie algebra, the results of [17] allow us to assert that there is only one solvable Lie algebra with maximal codimension of nilradical, which can be expressed in a suitable basis {x 1 , . .…”

Some cohomologically rigid solvable Leibniz algebras

“…An analogue of Mubarakzjanov's methods has been applied for solvable Leibniz algebras which shows the importance of the consideration of nilpotent Leibniz algebras and its nil-independent derivations [10] In the paper of [21] it is proved the following theorem. Theorem 6.…”