Related papers: Power-associative, conjugacy closed loops

It is known that with precision till isomorphism that only and only loops $M(F) = M_0(F)/<-1>$, where $M_0(F)$ denotes the loop, consisting from elements of all matrix Cayley-Dickson algebra $C(F)$ with norm 1, and $F$ be a subfield of…

Correlators of Wilson-line operators in non-abelian gauge theories are known to exponentiate, and their logarithms can be organised in terms of collections of Feynman diagrams called webs. In [1] we introduced the concept of Cweb, or…

$\mathrm{QAC}^0$ is the family of constant-depth polynomial-size quantum circuits consisting of arbitrary single qubit unitaries and multi-qubit Toffoli gates. It was introduced by Moore [arXiv: 9903046] as a quantum counterpart of…

The dissociation features in nuclear track emulsion of $^9$Be, $^{9,10}$C, and $^{12}$N nuclei of 1.2 A GeV energy are presented. The data presented for the nucleus $^9$Be can be considered as evidence that there is a core in its structure…

We propose that the physics beyond the standard Weinberg-Salam model is such that matter and the CP conjugate anti-matter fields have the same set of charges with respect to the various force groups (upto ordering). We show that this…

The conjugacy problem belongs to algorithmic group theory. It is the following question: given two words x, y over generators of a fixed group G, decide whether x and y are conjugated, i.e., whether there exists some z such that zxz^{-1} =…

Automorphic loops are loops in which all inner mappings are automorphisms. This variety of loops includes groups and commutative Moufang loops. A half-isomorphism $f : G \longrightarrow K$ between multiplicative systems $G$ and $K$ is a…

We introduce and study conjugate reversibility (or $c$-reversibility) in the complex special linear group $\SL(n,\C)$ where an element is conjugate to the inverse of its complex conjugate. We prove that in $\SL(n, \C)$, every $c$-reversible…

Let A_n be the alternating group on n letters. For n>5, we describe the elements alpha, beta in A_n when alpha^{A_n} beta^{A_n} is the union of at most four distinct conjugacy classes.

In groups, an abelian normal subgroup induces an abelian congruence. We construct a class of centrally nilpotent Moufang loops containing an abelian normal subloop that does not induce an abelian congruence. On the other hand, we prove that…

We present an exploratory study of structure of 13C, 15C, 17C and 19C, showing that the simple one-quasiparticle projected BCS (PBCS) model is capable to account for several important properties of these nuclei. Next we discuss the…

We develop some general ideas to study connected quandles of prime power size and we classify non-affine connected quandles of size $p^3$ for $p>3$, using a combination of group theoretical and universal algebraic tools. As a byproduct we…

Clifford circuits -- i.e. circuits composed of only CNOT, Hadamard, and $\pi/4$ phase gates -- play a central role in the study of quantum computation. However, their computational power is limited: a well-known result of Gottesman and…

The paper establishes an one-to-one correspondence between simple Moufang loops and Paige loops constructed over Galois extension over prime field in its algebraic closure. Using this connection it describes fully the family of…

Adapting a method recently proposed by C. Marboe and D. Volin for ${\cal N}$=4 super-Yang-Mills, we develop an algorithm for a systematic weak coupling expansion of the spectrum of anomalous dimensions in the $sl(2)$-like sector of planar…

Predictions of the spectroscopic properties of low-lying states are critical for nuclear structure studies, but are problematic for nuclei with an odd nucleon due to the interplay of the unpaired single particle with nuclear collective…

The Cayley-Dickson loop Q_n is the multiplicative closure of basic elements of the algebra constructed by n applications of the Cayley-Dickson doubling process (the first few examples of such algebras are real numbers, complex numbers,…

Let G be a connected reductive group over an algebraically closed field. We define a decomposition of G into finitely many strata such that each stratum is a union of conjugacy classes of fixed dimension; the strata are indexed by a set…

We compute the number of connected components in a generic real double Bruhat cell for series $B_n$ and $C_n$ and an exceptional group $F_4$.

We define a new variety of loops we call $\Gamma$-loops. After showing $\Gamma$-loops are power associative, our main goal will be showing a categorical isomorphism between Bruck loops of odd order and $\Gamma$-loops of odd order. Once this…