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Let $M_{n}$ be the multiplicative semigroup of all $n \times n$ complex matrices, and let $U_{n}$ and $G L_{n}$ be the $n$ –degree unitary group and general linear group over complex number field, respectively. We characterize group homomorphisms from $U_{n}$ to $G L_{m}$ when $n > m \geq 1$ or $n = m \geq 3$ , and thereby determine multiplicative homomorphisms from $U_{n}$ to $M_{m}$ when $n > m \geq 1$ or $n = m \geq 3$ . This generalize Hochwald’s result in [Lin. Alg. Appl. 212/213:339-351(1994)]: if $f : U_{n} \to M_{n}$ is a spectrum–preserving multiplicative homomorphism, then there exists a matrix $R$ in $G L_{n}$ such that $f (A) = R A R$ for...

Homomorphisms of group rings

Jan Krempa (1982)

Banach Center Publications

Homophonic quotients of free groups. (Quotients homophones des groupes libres.)

Mestre, Jean-François, Schoof, René, Washington, Lawrence, Zagier, Don (1993)

Experimental Mathematics

Homotopie des foncteurs en groupes.

Marcel Evrard (1979)

Mathematische Zeitschrift

Horocyclic products of trees

Laurent Bartholdi, Markus Neuhauser, Wolfgang Woess (2008)

Journal of the European Mathematical Society

Let $T_{1}, \dots, T_{d}$ be homogeneous trees with degrees $q_{1} + 1, \dots, q_{d} + 1 \geq 3$ , respectively. For each tree, let $𝔥 : T_{j} \to ℤ$ be the Busemann function with respect to a fixed boundary point (end). Its level sets are the horocycles. The horocyclic product of $T_{1}, \dots, T_{d}$ is the graph $𝖣𝖫 (q_{1}, \dots, q_{d})$ consisting of all $d$ -tuples $x_{1} \dots x_{d} \in T_{1} \times \dots \times T_{d}$ with $𝔥 (x_{1}) + \dots + 𝔥 (x_{d}) = 0$ , equipped with a natural neighbourhood relation. In the present paper, we explore the geometric, algebraic, analytic and probabilistic properties of these graphs and their isometry groups. If $d = 2$ and $q_{1} = q_{2} = q$ then we obtain a Cayley graph of the...

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Displaying 1 – 20 of 20

Hadamard spaces with isolated flats. (With an appendix written jointly with Mohamad Hindawi).

Hecke operators for GLₙ and buildings

Heuristics for the Whitehead minimization problem.

Homogeneous models and generic extensions.

Homogeneous verbal functions on groups

Homological and Topological Properties of Locally Indicable Groups.

Homological fixed point theorems

Homological Methods and the Third Dimension Subgroup

Homological Methods Applied to the Derived Series of Groups

Homological stability for automorphism groups of free groups.

Homology cylinders and the acyclic closure of a free group.

Homology stability for outer automorphism groups of free groups.

Homomorphisms from the unitary group to the general linear group over complex number field and applications

Homomorphisms of group rings

Homophonic quotients of free groups. (Quotients homophones des groupes libres.)

Homotopie des foncteurs en groupes.

Horocyclic products of trees

Hyperidentities and hypervarieties.

Hyperidentities of groups and semigroups.

Hyperidentities of groups and semigroups. (Short Communication).

Currently displaying 1 – 20 of 20