ﻻ يوجد ملخص باللغة العربية
In this paper, we study the metric geometric mean introduced by Pusz and Woronowicz and the spectral geometric mean introduced by Fiedler and Ptak, originally for positive definite matrices. The relation between $t$-metric geometric mean and $t$-spectral geometric mean is established via log majorization. The result is then extended in the context of symmetric space associated with a noncompact semisimple Lie group. For any Hermitian matrices $X$ and $Y$, Sos matrix exponential formula asserts that there are unitary matrices $U$ and $V$ such that $$e^{X/2}e^Ye^{X/2} = e^{UXU^*+VYV^*}.$$ In other words, the Hermitian matrix $log (e^{X/2}e^Ye^{X/2})$ lies in the sum of the unitary orbits of $X$ and $Y$. Sos result is also extended to a formula for adjoint orbits associated with a noncompact semisimple Lie group.
In this paper, we study the cup products and Betti numbers over cohomology superspaces of two-step nilpotent Lie superalgebras with coefficients in the adjoint modules over an algebraically closed field of characteristic zero. As an application, we p
In a recent preprint, Y. Namikawa proposed a conjecture on Q-factorial terminalizations and their birational geometry of nilpotent orbits. He proved his conjecture for classical simple Lie algebras. In this note, we prove his conjecture for exception
We show how the Connes-Moscovicis bialgebroid construction naturally provides universal objects for Lie algebras acting on non-commutative algebras.
We use a representation of a graded twisted tensor product of $K[x]$ with $K[y]$ in $L(K^{Bbb{N}_0})$ in order to obtain a nearly complete classification of these graded twisted tensor products via infinite matrices. There is one particular example a
We explicitly compute the adjoint L-function of those L-packets of representations of the group GSp(4) over a p-adic field of characteristic zero that contain non-supercuspidal representations. As an application we verify a conjecture of Gross-Prasad