The quantum geometry of supersymmetry and the generalized group extension problem

AbstractIn this article we state and prove precise theorems on the homotopy classification of graded categorical groups and their homomorphisms. The results use equivariant group cohomology, and they are applied to show a treatment of the general equivariant group extension problem.

Download Full-text

On Negligible and Absolutely Nonmeasurable Subsets of the Euclidean Plane

Georgian Mathematical Journal ◽

10.1515/gmj.2004.479 ◽

2004 ◽

Vol 11 (3) ◽

pp. 479-487

Author(s):

A. Kharazishvili

Keyword(s):

Euclidean Plane ◽

Identity Transformation ◽

Extension Problem ◽

Measure Extension ◽

Nonmeasurable Set

Abstract The notions of a negligible set and of an absolutely nonmeasurable set are introduced and discussed in connection with the measure extension problem. In particular, it is demonstrated that there exist subsets of the plane 𝐑2 which are 𝑇2-negligible and, simultaneously, 𝐺-absolutely nonmeasurable. Here 𝑇2 denotes the group of all translations of 𝐑2 and 𝐺 denotes the group generated by {𝑔} ∪ 𝑇2, where 𝑔 is an arbitrary rotation of 𝐑2 distinct from the identity transformation and all central symmetries of 𝐑2.

Download Full-text

Ground-state quantum geometry in superconductor–quantum dot chains

Physical Review B ◽

10.1103/physrevb.103.014516 ◽

2021 ◽

Vol 103 (1) ◽

Author(s):

R. L. Klees ◽

J. C. Cuevas ◽

W. Belzig ◽

G. Rastelli

Keyword(s):

Quantum Dot ◽

Ground State ◽

Quantum Geometry

Download Full-text

In Vacuo Dispersion-Like Spectral Lags in Gamma-Ray Bursts

Symmetry ◽

10.3390/sym13040541 ◽

2021 ◽

Vol 13 (4) ◽

pp. 541

Author(s):

Giovanni Amelino-Camelia ◽

Giacomo D’Amico ◽

Fabrizio Fiore ◽

Simonetta Puccetti ◽

Michele Ronco

Keyword(s):

Statistical Analysis ◽

Linear Correlation ◽

Gamma Ray ◽

Statistical Evidence ◽

Gamma Ray Bursts ◽

Quantum Geometry

Some recent studies exposed preliminary but rather intriguing statistical evidence of in vacuo dispersion-like spectral lags for gamma-ray bursts (GRBs), a linear correlation between time of observation and energy of GRB particles, which is expected in some models of quantum geometry. Those results focused on testing in vacuo dispersion for the most energetic GRB particles, and in particular only included photons with energy at emission greater than 40 GeV. We here extend the window of the statistical analysis down to 5 GeV and find results that are consistent with what had been previously noticed at higher energies.

Download Full-text

On the isometric extension problem

Quaestiones Mathematicae ◽

10.2989/16073606.2013.779953 ◽

2013 ◽

Vol 36 (3) ◽

pp. 321-330

Author(s):

Ruidong Wang

Keyword(s):

Extension Problem ◽

Isometric Extension

Download Full-text

On the End Extension Problem For Δ0-PA(S)

Mathematical Logic Quarterly ◽

10.1002/malq.19890350504 ◽

1989 ◽

Vol 35 (5) ◽

pp. 391-397

Author(s):

Henryk Kotlarski

Keyword(s):

Extension Problem

Download Full-text

AUTOMORPHISMS OF BRAID GROUPS ON S2, T2, P2 AND THE KLEIN BOTTLE K

Journal of Knot Theory and Its Ramifications ◽

10.1142/s0218216508005951 ◽

2008 ◽

Vol 17 (01) ◽

pp. 47-53 ◽

Cited By ~ 2

Author(s):

PING ZHANG

Keyword(s):

Braid Group ◽

Mapping Class Group ◽

Class Group ◽

Klein Bottle ◽

Closed Surface ◽

Group Extension ◽

Braid Groups ◽

Mapping Class ◽

Group B ◽

Central Automorphisms

It is shown that for the braid group Bn(M) on a closed surface M of nonnegative Euler characteristic, Out (Bn(M)) is isomorphic to a group extension of the group of central automorphisms of Bn(M) by the extended mapping class group of M, with an explicit and complete description of Aut (Bn(S2)), Aut (Bn(P2)), Out (Bn(S2)) and Out (Bn(P2)).

Download Full-text