The notion of an excellent quadratic form has been introduced by M. Knebusch 10, 11]. It has an obvious analogue for a semisimple linear algebraic group G over an arbitrary eld k: the group G is excellent if, for any eld extension K of k, the anisotropic kernel of the K-group G k K can be deened by a k-group. The aim of this paper is to investigate excellence properties of special linear and or...

Two classes of avalanche-finite matrices and their critical groups (integer cokernels) are studied from the viewpoint of chip-firing/sandpile dynamics, namely, the Cartan matrices of finite root systems and the McKay-Cartan matrices for finite subgroups G of general linear groups. In the root system case, the recurrent and superstable configurations are identified explicitly and are related to ...

Recently, codes over some special finite rings especially chain rings have been studied. More recently, codes over finite non-chain rings have been also considered. Study on codes over such rings or rings in general is motivated by the existence of some special maps called Gray maps whose images give codes over fields. Quantum error-correcting (QEC) codes play a crucial role in protecting quantum ...

We introduce a differential operator invariant under the special linear group SL(2n, C), and, as a consequence, the symplectic group Sp(2n, C). Connections with generalized Rankin–Cohen brackets for Siegel modular forms of genus n are sketched.

wide range of planar structures in new technologies has attracted special consideration. in this research vibration behavior of plates with non-linear edges is investigated by means of finite difference (fd) method. for this issue, classical and analytical solutions for plates with linear edges were analyzed and mutual equations, needed for numerical calculation were extracted. by expanding the...

Magueijo and Smolin have introduced a modification of the Lorentz group for the momentum-space transformations in Doubly-Special Relativity. As presented the group is non-linear, but we show that it is a group of fraction-linear transformations in 4 dimensional real projective space. We pass to the associated 5 dimensional linear space and identify the subgroup as a conjugate of the ordinary Lo...