Results 41 to 50 of about 55,229 (134)

Quantum affine transformation group and covariant differential calculus

, 1993
We discuss quantum deformation of the affine transformation group and its Lie algebra. It is shown that the quantum algebra has a non-cocommutative Hopf algebra structure, simple realizations and quantum tensor operators.
Aizawa, N., Sato, H. -T.
core   +2 more sources

Equivariant toric geometry and Euler–Maclaurin formulae

Communications on Pure and Applied Mathematics, Volume 79, Issue 3, Page 451-557, March 2026.
Abstract We first investigate torus‐equivariant motivic characteristic classes of toric varieties, and then apply them via the equivariant Riemann–Roch formalism to prove very general Euler–Maclaurin‐type formulae for full‐dimensional simple lattice polytopes.
Sylvain E. Cappell, Laurenţiu Maxim, Jörg Schürmann, Julius L. Shaneson   +3 more
wiley   +1 more source

Solving Particle–Antiparticle and Cosmological Constant Problems

Axioms
We solve the particle-antiparticle and cosmological constant problems proceeding from quantum theory, which postulates that: various states of the system under consideration are elements of a Hilbert space H with a positive definite metric; each physical
Felix M. Lev
doaj   +1 more source

On quantum ergodicity for higher‐dimensional cat maps modulo prime powers

Bulletin of the London Mathematical Society, Volume 58, Issue 3, March 2026.
Abstract A discrete model of quantum ergodicity of linear maps generated by symplectic matrices A∈Sp(2d,Z)$A \in \operatorname{Sp}(2d,{\mathbb {Z}})$ modulo an integer N⩾1$N\geqslant 1$, has been studied for d=1$d=1$ and almost all N$N$ by Kurlberg and Rudnick (2001, Comm. Math. Phys., 222, 201–227).
Subham Bhakta, Igor E. Shparlinski
wiley   +1 more source

Lax Integrable Supersymmetric Hierarchies on Extended Phase Spaces

Symmetry, Integrability and Geometry: Methods and Applications, 2006
We obtain via Bäcklund transformation the Hamiltonian representation for a Lax type nonlinear dynamical system hierarchy on a dual space to the Lie algebra of super-integral-differential operators of one anticommuting variable, extended by evolutions of ...
Oksana Ye. Hentosh
doaj  

Star Product and Invariant Integration for Lie type Noncommutative Spacetimes

, 2007
We present a star product for noncommutative spaces of Lie type, including the so called ``canonical'' case by introducing a central generator, which is compatible with translations and admits a simple, manageable definition of an invariant integral.
A. Sykora, A.H. Fatollahi, C. Chryssomalakos, Chryssomalis Chryssomalakos, Elias Okon, J. Wess, J.M. Gracia-Bondia, L. Moller, M. Daszkiewicz, M. Dimitrijevic, S. Kurkcuoglu, S. Majid, S. Meljanac, V. Kathotia   +13 more
core   +1 more source

On the Euler characteristic of S$S$‐arithmetic groups

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract We show that the sign of the Euler characteristic of an S$S$‐arithmetic subgroup of a simple algebraic group depends on the S$S$‐congruence completion only, except possibly in type 6D4${}^6 D_4$. Consequently, the sign is a profinite invariant for such S$S$‐arithmetic groups with the congruence subgroup property. This generalizes previous work
Holger Kammeyer, Giada Serafini
wiley   +1 more source

Completeness and Cocompleteness Transfer for Internal Group Objects with Geometric Obstructions

Mathematics
This work establishes definitive conditions for the inheritance of categorical completeness and cocompleteness by categories of internal group objects.
Jian-Gang Tang, Nueraminaimu Maihemuti, Jia-Yin Peng, Yimamujiang Aisan, Ai-Li Song   +4 more
doaj   +1 more source

Toral symmetries of collapsed ancient solutions to the homogeneous Ricci flow

Journal of the London Mathematical Society, Volume 113, Issue 3, March 2026.
Abstract Collapsed ancient solutions to the homogeneous Ricci flow on compact manifolds occur only on the total space of principal torus bundles. Under an algebraic assumption that guarantees flowing through diagonal metrics and a tameness assumption on the collapsing directions, we prove that such solutions have additional symmetries, that is, they ...
Anusha M. Krishnan, Francesco Pediconi, Sammy Sbiti   +2 more
wiley   +1 more source

Optimally defined Racah-Casimir operators for su(n) and their eigenvalues for various classes of representations

, 2000
This paper deals with the striking fact that there is an essentially canonical path from the $i$-th Lie algebra cohomology cocycle, $i=1,2,... l$, of a simple compact Lie algebra $\g$ of rank $l$ to the definition of its primitive Casimir operators $C ...
A. J. Macfarlane, de Azcárraga J.A., Dynkin E.B., J. A. de Azcárraga, Kuriyan J.G., Macfarlane A.J., Macfarlane A.J., Okubo S., Patera J., Sudbery A., van Ritbergen T.   +10 more
core   +2 more sources