A subalgebra H of a finite dimensional Lie algebra L is said to be a SCAP-subalgebra if there is a chief series 0 = L0 \subset L1 \subset...\subset Lt = L of L such that for every i = 1, 2,..., t, we have H + Li = H + Li-1 or H ∩ Li = H ∩ Li-1. This is analogous to the concept of SCAP-subgroup, which has been studied by a number of authors. In this article, we investigate the connection between the structure of a Lie algebra and its SCAP-subalgebras and give some sufficient conditions for a Lie algebra to be solvable or supersolvable., Sara Chehrazi, Ali Reza Salemkar., and Obsahuje seznam literatury
We consider separately radial (with corresponding group ${\mathbb{T}}^n$) and radial (with corresponding group
${\rm U}(n))$ symbols on the projective space ${\mathbb{P}^n({\mathbb{C}})}$, as well as the associated Toeplitz operators on the weighted Bergman spaces. It is known that the $C^*$-algebras generated by each family of such Toeplitz operators are commutative (see R. Quiroga-Barranco and A. Sanchez-Nungaray (2011)). We present a new representation theoretic proof of such commutativity. Our method is easier and more enlightening as it shows that the commutativity of the $C^*$-algebras is a consequence of the existence of multiplicity-free representations. Furthermore, our method shows how to extend the current formulas for the spectra of the corresponding Toeplitz operators to any closed group lying between ${\mathbb{T}}^n$ and ${\rm U}(n)$., Raul Quiroga-Barranco, Armando Sanchez-Nungaray., and Obsahuje bibliografii
We determine in \mathbb{R}^{n} the form of curves C corresponding to strictly monotone functions as well as the components of affine connections \Delta for which any image of C under a compact-free group Ω of affinities containing the translation group is a geodesic with respect to \Delta . Special attention is paid to the case that Ω contains many dilatations or that C is a curve in \mathbb{R}^{3}. If C is a curve in \mathbb{R}^{3} and Ω is the translation group then we calculate not only the components of the curvature and the Weyl tensor but we also decide when \Delta yields a flat or metrizable space and compute the corresponding metric tensor., Josef Mikeš, Karl Strambach., and Obsahuje seznam literatury
Let (M, g) be a 4-dimensional Einstein Riemannian manifold. At each point p of M, the tangent space admits a so-called Singer-Thorpe basis (ST basis) with respect to the curvature tensor R at p. In this basis, up to standard symmetries and antisymmetries, just 5 components of the curvature tensor R are nonzero. For the space of constant curvature, the group O(4) acts as a transformation group between ST bases at TpM and for the so-called 2-stein curvature tensors, the group Sp(1) ⊂ SO(4) acts as a transformation group between ST bases. In the present work, the complete list of Lie subgroups of SO(4) which act as transformation groups between ST bases for certain classes of Einstein curvature tensors is presented. Special representations of groups SO(2), T2, Sp(1) or U(2) are obtained and the classes of curvature tensors whose transformation group into new ST bases is one of the mentioned groups are determined., Zdeněk Dušek, Hradec Králové., and Obsahuje seznam literatury
Magdalena Morgese Borys, Petr Zemčík., České resumé, Projekt je financován Evropským sociálním fondem, rozpočtem hl. města Prahy a státním rozpočtem, and born digital
A ring R is called a right PS-ring if its socle, Soc(RR), is projective. Nicholson and Watters have shown that if R is a right PS-ring, then so are the polynomial ring R[x] and power series ring R[[x]]. In this paper, it is proved that, under suitable conditions, if R has a (flat) projective socle, then so does the skew inverse power series ring R[[x−1; alfa, delta]] and the skew polynomial ring R[x; alfa, delta], where R is an associative ring equipped with an automorphism and an alfa-derivation delta. Our results extend and unify many existing results. Examples to illustrate and delimit the theory are provided., Kamal Paykan., and Seznam literatury
We obtain a conditional, under the Generalized Riemann Hypothesis, lower bound on the number of distinct elliptic curves E over a prime finite field F_{p} of p elements, such that the discriminant D(E) of the quadratic number field containing the endomorphism ring of E over F_{p} is small. For almost all primes we also obtain a similar unconditional bound. These lower bounds complement an upper bound of F. Luca and I.E. Shparlinski (2007)., Igor E. Shparlinski., and Obsahuje seznam literatury