2,309 research outputs found
b-Structures on Lie groups and Poisson reduction
No full textMotivated by the group of Galilean transformations and the subgroup of Galilean transformations which fix time zero, we introduce the notion of a b-Lie group as a pair (G, H) where G is a Lie group and H is a codimension-one Lie subgroup. Such a notion allows us to give a theoretical framework for transformations of space-time where the initial time can be seen as a boundary. In this theoretical framework, we develop the basics of the theory and study the associated canonical b-symplectic structure on the b-cotangent bundle T-b *G together with its reduction theory. Namely, we extend the minimal coupling procedure to T-b *G/H and prove that the Poisson reduction under the cotangent lifted action of H by left translations can be described in terms of the Lie Poisson structure on h* (where h is the Lie algebra of H) and the canonical b-symplectic structure on T-b *(G/H), where G/H is viewed as a one-dimensional b-manifold having as critical hypersurface (in the sense of b-manifolds) the identity element. (C) 2022 The Author(s). Published by Elsevier B.V.PD
SMARANDACHE NON-ASSOCIATIVE RINGS
No full textAn associative ring is just realized or built using reals or complex; finite or infinite
by defining two binary operations on it. But on the contrary when we want to define or study or even introduce a non-associative ring we need two separate algebraic structures say a commutative ring with 1 (or a field) together with a loop or a groupoid or a vector space or a linear algebra. The two non-associative well-known algebras viz. Lie algebras and Jordan algebras are mainly built using a vector space over a field satisfying special identities called the Jacobi identity and Jordan identity respectively. Study of these algebras started as early as 1940s. Hence the study of non-associative algebras or even non-associative rings boils down to the study of properties of vector spaces or linear algebras over fields
Lie tori of rank 1
No full textThis article is based on a talk presented by the first author at the conference on Lie and Jordan Algebras, their Representations and Applications held in Guarujá, Brazil in May 2004. The article surveys some recent progress by a number of authors in the study of extended affine Lie algebras and some closely related Lie algebras called Lie tori
Measuring Adjoint-invariance of Neighborhoods in Solvable Lie Groups
No full textIn this thesis, we derive a lower bound on a quantity appearing in a Fourier multiplier inequality on solvable Lie groups.In Caspers, Janssens, Krishnaswamy-Usha and Miaskiwskyi (2022), a classical result by de Leeuw about the restriction of Fourier multipliers on to a discrete subgroup is extended to a noncommutative setting. It is shown that a compactly supported -multiplier on a locally compact group has the following relation to its restriction to a discrete subgroup :c(\operatorname{supp}(m|_{\Gamma})) \norm{T_{m|_{\Gamma}}}_p \leq \norm{T_m}_p.Here , where is a quantity that determines to what extent small neighborhoods of the identity in are left invariant by conjugation by elements of . In this thesis, we estimate for connected solvable Lie groups.\\Our main result is theorem 9, which states that for a connected solvable Lie group with Lie algebra \g, if \lambda_1,\ldots,\lambda_n\colon \g_{\mathbb{C}}\to\mathbb{C} are the generalized weights of the complexification \g_{\mathbb{C}}, there exist unique homomorphisms \chi_1,\ldots,\chi_n\colon G\to\mathbb{R}_{>0} such that , and Applied Mathematic
C-sections of Lie algebras
No full textLet M be a maximal subalgebra of a Lie algebra L and A/B a chief factor of L such that B ⊆ M and A ⊄ M. We call the factor algebra M ∩ A/B a c-section of M. All such c-sections are isomorphic, and this concept is related those of c-ideals and ideal index previously introduced by the author. Properties of c-sections are studied and some new characterizations of solvable Lie algebras are obtained
Reduced-rank adaptive least bit-error-rate detection in hybrid direct-sequence time-hopping ultrawide bandwidth systems
No full textDesign of high-efficiency low-complexity detection schemes for ultrawide bandwidth (UWB) systems is highly challenging. This contribution proposes a reduced-rank adaptive multiuser detection (MUD) scheme operated in least bit-errorrate (LBER) principles for the hybrid direct-sequence timehopping UWB (DS-TH UWB) systems. The principal component analysis (PCA)-assisted rank-reduction technique is employed to obtain a detection subspace, where the reduced-rank adaptive LBER-MUD is carried out. The reduced-rank adaptive LBERMUD is free from channel estimation and does not require the knowledge about the number of resolvable multipaths as well as the knowledge about the multipaths’ strength. In this contribution, the BER performance of the hybrid DS-TH UWB systems using the proposed detection scheme is investigated, when assuming communications over UWB channels modeled by the Saleh-Valenzuela (S-V) channel model. Our studies and performance results show that, given a reasonable rank of the detection subspace, the reduced-rank adaptive LBER-MUD is capable of efficiently mitigating the multiuser interference (MUI) and inter-symbol interference (ISI), and achieving the diversity gain promised by the UWB systems
Cohomological local-to-global principles and integration in finite- and infinite-dimensional Lie theory
No full textThe subject of this thesis is twofold: The first part is the study of local-to-global principles for the continuous Lie algebra (co-)homology of certain infinite-dimensional Lie algebras of geometric origin, specifically, Gelfand-Fuks cohomology and continuous cohomology of gauge algebras. It includes both an exposition to classical results of Gelfand and Fuks, and new methods to construct general local-to-global spectral sequences for the Lie algebra cohomology of section spaces of Lie algebroids. This includes a close functional-analytics study of the involved spaces and attention to complications within LF- and Fréchet spaces. The second part contains a study of two certain measure-theoretic problems on Lie groups. The first such problem is the study of Haar measures of certain identity-neighbourhoods relevant to de Leeuw inequalities in Harmonic Analysis. The second problem is the evaluation of expectation values of polynomials on compact Lie groups, motivated by the study of Weingarten functions and Wilson loops from lattice gauge theory.Analysi
The Social Desirability Scale-17 (SDS-17): Convergent validity, discriminant validity, and relationship with age
No full textFour studies are presented investigating the convergent validity, discriminant validity, and relationship with age of the Social Desirability Scale-17 (SDS-17). As to convergent validity, SDS-17 scores showed correlations between .52 and .85 with other measures of social desirability (Eysenck Personality Questionnaire-Lie Scale, Sets of Four Scale, Marlowe-Crowne Scale). Moreover, scores were highly sensitive to social-desirability-provoking instructions (job-application instruction). Finally, with respect to the Balanced Inventory of Desirable Responding, SDS-17 scores showed a unique correlation with impression management, but not with self-deception. As to discriminant validity, SDS-17 scores showed nonsignificant correlations with neuroticism, extraversion, psychoticism, and openness to experience, whereas there was some overlap with agreeableness and conscientiousness. With respect to relationship with age, the SDS-17 was administered in a sample stratified for age, with age ranging from 18 to 89 years. In all but the oldest age group, the SDS-17 showed substantial correlations with the Marlowe-Crowne Scale. The influence of age (cohort) on mean scores, however, was significantly smaller for the SDS-17 than for the Marlowe-Crowne Scale. In sum, results indicate that the SDS-17 is a reliable and valid measure of social desirability, suitable for adults of 18 to 80 years of age
Integrability of central extensions of the Poisson Lie algebra via prequantization
No full textWe present a geometric construction of central S 1-extensions of the quantomorphism group of a prequantizable, compact, symplectic manifold, and explicitly describe the corresponding lattice of integrable cocycles on the Poisson Lie algebra. We use this to find nontrivial central S 1-extensions of the universal cover of the group of Hamiltonian diffeomorphisms. In the process, we obtain central S1-extensions of Lie groups that act by exact strict contact transformations. Analysi
On a Lie-theoretic Approach to Generalized Doubly Stochastic Matrices and Applications
No full textIn this article, we study generalized doubly stochastic matrices using the theory of Lie groups and Lie algebras. Applications to the inverse eigenvalue problem for symmetric doubly stochastic matrices are presented.ATIYAH M, 1982, B LOND MATH SOC, V23, P1; ATIYAH MF, 1983, P EDINBURGH MATH SOC, V26, P121; Audin M, 1991, TOPOLOGY TORUS ACTIO; BAUERLE GG, 1990, FINITE INFINITE DIME; BRUALDI RA, 1988, LINEAR ALGEBRA APPL, V107, P77, DOI 10.1016-0024-3795(88)90239-X; BRUALDI RA, 1991, ENCY MATH; CRUSE AB, 1975, DISCRETE MATH, V13, P109, DOI 10.1016-0012-365X(75)90012-6; GIBSON PM, 1980, LINEAR ALGEBRA APPL, V30, P101, DOI 10.1016-0024-3795(80)90185-8; GOURDIN M, 1982, BASICS LIE GROUPS; Helgason S., 1984, GROUPS GEOMETRIC ANA; JOHNSEN EC, 1971, LINEAR ALGEBRA APPL, V4, P225; Johnson C., 1981, LINEAR MULTILINEAR A, V10, P113, DOI 10.1080-03081088108817402; Katz M, 1970, J COMB THEORY, V8, P417, DOI 10.1016-S0021-9800(70)80034-5; Kirillov A.A., 1976, ELEMENTS THEORY REPR; Kostant B., 1973, ANN SCI ECOLE NORM S, p[6, 413]; Minc H., 1988, NONNEGATIVE MATRICES; MOURAD BH, 1998, THESIS U NEW S WALES; Perfect H., 1965, MONATSH MATH, V69, P35, DOI 10.1007-BF01313442; SINKHORN R, 1962, NOT AM MATH SOC, V9, P334; Soules G., 1983, LINEAR MULTILINEAR A, V13, P241, DOI 10.1080-03081088308817523; Tam T.Y., 1997, LINEAR MULTILINEAR A, V43, P87, DOI 10.1080-030810897088185188101
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