Related papers: Constructive homomorphisms for classical groups

We describe a construction that to each algebraically specified notion of higher-dimensional category associates a notion of homomorphism which preserves the categorical structure only up to weakly invertible higher cells. The construction…

We present a fast algorithm to compute the Delta set of a nonsymmetric numerical semigroups with embedding dimension three.

Given a strict partial order $\Delta$ on a set $\Lambda$ and an arbitrary ring $R$ with $1\neq 0$, the corresponding McLain group $M(\Delta)$ has been studied in depth. We construct a larger family of McLain groups $G(\Delta)$, where…

We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector…

Let $G$ be a complex classical group, and let $V$ be its defining representation (possibly plus a copy of the dual). A foundational problem in classical invariant theory is to write down generators and relations for the ring of…

These notes describe some links between the group $\mathrm{SL}_2(\mathbb{R})$, the Heisenberg group and hypercomplex numbers---complex, dual and double numbers. Relations between quantum and classical mechanics are clarified in this…

Topological data analysis (TDA) is a rapidly growing area that applies techniques from algebraic topology to extract robust features from large-scale data. A key task in TDA is the estimation of (normalized) Betti numbers, which capture…

In this paper a finite dimensional unital associative algebra is presented, and its group of algebra automorphisms is detailed. The studied algebra can physically be understood as the creation operator algebra in a formal quantum field…

The main component of (constructive) recognition algorithms for black box groups of Lie type in computational group theory is the construction of unipotent elements. In the existing algorithms unipotent elements are found by random search…

The second-order differential equation describes harmonic oscillators, as well as currents in LCR circuits. This allows us to study oscillator systems by constructing electronic circuits. Likewise, one set of closed commutation relations…

Let K be a number field, let A be a finite dimensional semisimple K-algebra and let Lambda be an O_K-order in A. It was shown in previous work that, under certain hypotheses on A, there exists an algorithm that for a given (left)…

We use the Sigma^1_3 absoluteness theorem to show that the complexity of the statement "(omega,E)$ is isomorphic to an initial segment of the core model" is Pi^1_4, and that the complexity of the statement "(omega,E)$ is isomorphic to a…

We study a class of evolutionary partial differential systems with two components related to second order (in time) non-evolutionary equations of odd order in spatial variable. We develop the formal diagonalisation method in symbolic…

We give elementary applications of quasi-homomorphisms to growth problems in groups. A particular case concerns the number of torsion elements required to factorise a given element in the mapping class group of a surface.

We show that for algebraic groups over local fields of characteristic zero, the following are equivalent: Every homomorphism has a closed image, every unitary representation decomposes into a direct sum of finite-dimensional and mixing…

Using group actions and orbit-stabilizer methods, we study the geometry of isomorphism classes of finite-dimensional $\omega$-Lie algebras over a field $\mathbb{K}$ of characteristic $\neq 2$ and establish a one-to-one correspondence…

This paper gives an explicit structure theorem for the symmetric group acting on the symmetric algebra of its natural module. Let $G$ be the symmetric group on $x_1,..., x_n$ and let $d_i$ be the $i^{\text{th}}$ elementary symmetric…

This manuscript represents the author's PhD dissertation thesis.The first part studies decision problems in Thompson's groups F,T,V and some generalizations. The simultaneous conjugacy problem is determined to be solvable for Thompson's…

For any positive integer $N$, we describe a natural complex representation of the symmetric group $\Sigma_N$ on the vector space spanned by its involutions that contains each irreducible representation exactly once.

Developing an idea of Kapranov and Voevodsky, we introduce a model of weak omega-categories based on directed complexes, combinatorial presentations of pasting diagrams. We propose this as a convenient framework for higher-dimensional…