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Structures of automorphisms and automorphism groups in fuzzy set theory are studied in detail in view of applications to synonymy and antonymy representations.

Representations of the general linear group over symmetry classes of polynomials

Yousef Zamani, Mahin Ranjbari (2018)

Czechoslovak Mathematical Journal

Let $V$ be the complex vector space of homogeneous linear polynomials in the variables $x_{1}, ..., x_{m}$ . Suppose $G$ is a subgroup of $S_{m}$ , and $χ$ is an irreducible character of $G$ . Let $H_{d} (G, χ)$ be the symmetry class of polynomials of degree $d$ with respect to $G$ and $χ$ . For any linear operator $T$ acting on $V$ , there is a (unique) induced operator $K_{χ} (T) \in End (H_{d} (G, χ))$ acting on symmetrized decomposable polynomials by $K_{χ} (T) (f_{1} * f_{2} * ... * f_{d}) = T f_{1} * T f_{2} * ... * T f_{d} .$ In this paper, we show that the representation $T \mapsto K_{χ} (T)$ of the general linear group $G L (V)$ is equivalent to the direct sum of $χ (1)$ copies of a representation...

Representations of the generalized symmetric groups.

Can, Himmet (1996)

Beiträge zur Algebra und Geometrie

Representing Countable Groups by Homeomorphism Groups in Hilbert Space.

Jan van Mill (1982)

Mathematische Annalen

Representing lattices by homotopy groups of graphs

Jiří Tůma (1999)

Commentationes Mathematicae Universitatis Carolinae

In this paper we represent every lattice by subgroups of free groups using the concept of the homotopy group of a graph.

Representing subgroups of finitely presented groups by quotient subgroups.

Hulpke, Alexander (2001)

Experimental Mathematics

R-equivalence and rationality problem for semisimple adjoint classical algebraic groups

Alexander S. Merkurjev (1996)

Publications Mathématiques de l'IHÉS

Rescuing the Whitehead Method for Free Products, I: Peak Reduction.

Donald J. Collins, Zieschang Heiner (1984)

Mathematische Zeitschrift

Rescuing the Whitehead Method for Free Products, II: The Algorithm.

Heiner Zieschang, Donald J. Collins (1984)

Mathematische Zeitschrift

Réseaux de Coxeter-Davis et commensurateurs

Frédéric Haglund (1998)

Annales de l'institut Fourier

For each integer $k \geq 6$ and each finite graph $L$ , we construct a Coxeter group $W$ and a non positively curved polygonal complex $A$ on which $W$ acts properly cocompactly, such that each polygon of $A$ has $k$ edges, and the link of each vertex of $A$ is isomorphic to $L$ . If $L$ is a “generalized $m$ -gon”, then $A$ is a Tits building modelled on a reflection group of the hyperbolic plane. We give a condition on $Aut (L)$ for $Aut (A)$ to be non enumerable (which is satisfied if $L$ is a thick classical generalized $m$ -gon). On the other hand,...

Residual ...-Centrality in Groups.

Terence E. Stanley (1972)

Mathematische Zeitschrift

Residual finiteness in completely regular semigroup varieties.

P.G. Trotter, F.J. Pastijn (1988)

Semigroup forum

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