ﻻ يوجد ملخص باللغة العربية
The purpose of this note is to discuss a few lines appearing in the work of late Fantappi`e. They concern the proof of rigidity of a specific real semisimple Lie algebra: ${mathfrak O}(4,1)$. Our intention is to discuss to what extent such proof constitutes a missed opportunity in history of post-war Italian mathematics.
It is shown that the orbits of the space of local deformations of the Lie algebra $bar{A_5}$ over an algebraically closed field $K$ of characteristic 2 with respect to the automorphism group $mathrm{PGL} (6)$ correspond to $mathrm{GL} (V)$-orbits of
In mathematical aspect, we introduce quantum algorithm and the mathematical structure of quantum computer. Quantum algorithm is expressed by linear algebra on a finite dimensional complex inner product space. The mathematical formulations of quantum
We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $leq 11$. For dimensions $D=10,11
We study deformations of Lie groupoids by means of the cohomology which controls them. This cohomology turns out to provide an intrinsic model for the cohomology of a Lie groupoid with values in its adjoint representation. We prove several fundamenta
We define a supersymmetric quantum mechanics of fermions that take values in a simple Lie algebra. We summarize what is known about the spectrum and eigenspaces of the Laplacian which corresponds to the Koszul differential d. Firstly, we concentrate