$ G$-identities of non-associative algebras

Abstract

A magnetically shielded sampling technique is developed which permits determination of plasma parameters by orifice probe, electrostatic analyser or mass spectrometer for medium-pressure magnetised plasmas. Experimental results show that: (i) for a retarded-electron current we do not observe any abnormal peak and non-exponential potential dependence of current potential characteristics as observed by previous orifice probe measurements in a magnetised plasma; (ii) electron temperature measurements agree to within 10 ;g with recent positive-column electron temperature theory; (iii) plasma density measurements agree to within a factor of 3 with electrostatic probe measurements.Abstract We describe a method of gating the emission from the laser-produced plasmas of solid targets. A Pockels cell is operated between parallel polarisers and used as an optical shutter. If the shutter is opened after the continuum and multiply ionised species emission has subsided, a considerably simplified spectrum containing only singly ionised and atomic lines is obtained. Gated spectra from Mg, A1 and Fe plasmas are shown.

Algebras with involution with linear codimension growth

“…A direct computation shows that f T (n−2,1) ,T (1) (s 1 , s 2 , k 1 ) = −e 13 = 0. Hence f T (n−2,1) ,T (1) / ∈ Id * (M 4 ) and c * n (M 4 ) deg χ λ,μ = n 1 deg χ λ deg χ μ = n(n − 2). 2…”

“…be the corresponding highest weight vector. Now we exhibit a non-zero evaluation of f T (n−2,1) ,T (1) . Consider s 1 = e 11 + e 33 , s 2 = e 12 + e 23 and k 1 = e 12 − e 23 .…”

“…Moreover, an explicit bound related to the ordinary identities of the ✩ Research partially supported by MIUR of Italy. algebra A was found in [1]. In case of polynomial growth, the following characterization was given in [7]: the * -codimension sequence of an algebra A is polynomially bounded if and only if its * -identities are not a consequence of the * -identities of F ⊕ F , endowed with the exchange involution, and of M, a suitable 4-dimensional subalgebra of the algebra of 4 × 4 upper triangular matrices.…”

Algebras simple with respect to a Taft algebra action

“…In [14], the author classified all finite dimensional H 4 (−1)-simple algebras. Here we classify finite dimensional H m 2 (ζ)-simple algebras over an algebraically closed field (Sections 2-3).Amitsur's conjecture on asymptotic behaviour of codimensions of ordinary polynomial identities was proved by A. Giambruno and M. V. Zaicev [10, Theorem 6.5.2] in 1999.Suppose an algebra is endowed with a grading, an action of a group G by automorphisms and anti-automorphisms, an action of a Lie algebra by derivations or a structure of an Hmodule algebra for some Hopf algebra H. Then it is natural to consider, respectively, graded, G-, differential or H-identities [1,2,4,7,15].The analog of Amitsur's conjecture for polynomial H-identities was proved under wide conditions by the author in [12,13]. However, in those results the H-invariance of the Jacobson radical was required.…”

“…Giambruno Suppose an algebra is endowed with a grading, an action of a group G by automorphisms and anti-automorphisms, an action of a Lie algebra by derivations or a structure of an Hmodule algebra for some Hopf algebra H. Then it is natural to consider, respectively, graded, G-, differential or H-identities [1,2,4,7,15].…”