Related papers: Power-associative, conjugacy closed loops

We study the s-wave quintet Cooper pairing phase ($S_{tot}=2$) in spin-3/2 cold atomic systems and identify various novel features which do not appear in the spin-1/2 counterpart. A single quantum vortex is shown to be energetically less…

The study is aimed at revealing the most important substructures (fragments) of polyenes with heteroatoms determining the alteration in the conjugation energy of the whole compound due to substitution and the relevant charge redistribution.…

For $n\geq 2$ we compute the homotopy groups of $(n-1)$-connected closed manifolds of dimension $(2n+1)$. Away from the finite set of primes dividing the order of the torsion subgroup in homology, the $p$-local homotopy groups of $M$ are…

A conjecture of Kac now a theorem asserts that the polynomial now known as the Kac polynomial, which counts the isomorphism classes of absolutely indecomposable representations of a quiver over a finite field with a given dimension vector,…

The causal representation of multi-loop scattering amplitudes, obtained from the application of the loop-tree duality formalism, comprehensively elucidates, at integrand level, the behaviour of only physical singularities. This…

The existence of an extremal self-dual binary linear code C of length 72 is a long-standing open problem. We continue the investigation of its automorphism group: looking at the combination of the subcodes fixed by different involutions and…

The isomorphism problem for centrally nilpotent loops can be tackled by methods of cohomology. We develop tools based on cohomology and linear algebra that either lend themselves to direct count of the isomorphism classes (notably in the…

The iterative qubit coupled cluster (iQCC) method is a systematic variational approach to solve the electronic structure problem on universal quantum computers. It is able to use arbitrarily shallow quantum circuits at expense of iterative…

We investigate Moufang loops which can be written as the semidirect product of a loop and a group. We also examine a particular class of loop extensions which arise as a result of a finite cyclic group acting as a group of semiautomorphisms…

We introduce the notion of the power quandle of a group, an algebraic structure that forgets the multiplication but keeps the conjugation and the power maps. Compared with plain quandles, power quandles are much better invariants of groups.…

We characterize the group property of being with infinite conjugacy classes (or icc, i.e. in which all conjugacy classes beside 1 are infinite) for split extensions of groups.

Nonassociative finite simple Moufang loops are exactly the loops constructed by Paige from Zorn vector matrix algebras. We prove this result anew, using geometric loop theory. In order to make the paper accessible to a broader audience, we…

We study quasi-semisimple elements of disconnected reductive algebraic groups over an algebraically closed field. We describe their centralizers, define isolated and quasi-isolated quasi-semisimple elements and classify their conjugacy…

We study the dynamics of correlations in a paradigmatic setup to observe $\mathcal{PT}$-symmetric physics: a pair of coupled oscillators, one subject to a gain one to a loss. Starting from a coherent state, quantum correlations (QCs) are…

In this work, we investigate the possibility of improving multireference-driven coupled cluster (CC) approaches with an algorithm that iteratively combines complete active space (CAS) calculations with tailored CC and externally corrected…

This work identifies a solvable (in the sense that spectral correlation functions can be expressed in terms of orthogonal polynomials), rotationally invariant random matrix ensemble with a logarithmic weakly confining potential. The…

We show that the parity of more than three non-target input bits cannot be computed by QAC-circuits of depth-2, not even uncleanly, regardless of the number of ancilla qubits. This result is incomparable with other recent lower bounds on…

We report on recent progress on five-loop calculations in perturbative QCD. We discuss the computation of the perturbative quark condensate, decoupling in QCD, and the precision determination of charm and bottom quark masses. For the…

Connectivity is a homotopy invariant property of separable C*-algebras which has three notable consequences: absence of nontrivial projections, quasidiagonality and a more geometric realization of KK-theory for nuclear C*-algebras using…

The structure of the commutative Moufang loops (CML) with minimum condition for subloops is examined. In particular it is proved that such a CML $Q$ is a finite extension of a direct product of a finite number of the quasicyclic groups,…