The index of nilpotent Lie poset algebras

The evolution of the spectrum of a Frobenius Lie algebra under deformation

“…However, we have no examples of deformable Frobenius Lie poset algebras. It is also worth noting that the unbroken spectrum property seems to be a property of Frobenius Lie poset algebras, although the spectrum is "binary", consisting of only 0's and 1's (see [8], [9], [10], and [11]).…”

Identities and derived lengths of finitary incidence algebras and their group of units

“…Recently, a special attention has been paid to the associated Lie algebra [2,3] and linear maps on it [8,9,10,11,37]. Feinberg [7] proved that the incidence algebra of a locally finite quasiordered set X over a field satisfies a polynomial identity if and only of X is bounded.…”

The Index and Spectrum of Lie Poset Algebras of Types B, C, and D

“…The development of combinatorial index formulas for certain families of Lie algebras is of current interest. Families for which such formulas have been found include seaweed algebras and type-A Lie poset algebras (see [4,5,6,8,9,12,17,19,20,21]). In this article, we consider the analogues of type-A Lie poset algebras in the other classical types: B k = so(2k + 1), C k = sp(2k), and D k = so(2k); such algebras are called type-B, C, and D Lie poset algebras, respectively.…”