The set of all (n×n) non-singular matrices over the field F. And this forms a group under operation matrix multiplication. This is called general linear dimension F, denoted by . determinant these homomorphism from into F* and kernel was special Thus subgroup which contains one. rationally valued characters rational representations are written as combination induced for groups discussed in pape...

We study the complexity of structurally restricted homomorphism and constraint satisfaction problems. For every class of relational structures C, let LHOM(C, _) be the problem of deciding whether a structure A ∈ C has a homomorphism to a given arbitrary structure B, when each element in A is only allowed a certain subset of elements of B as its image. We prove, under a certain complexity-theore...

generators. Our goal is to make this description more concrete. Note that G(k, n) = U(n)/(U(k)×U(n− k)) = St(k, n)/U(k) is the quotient by U(k) of the complex Stiefel manifold St(k, n) of partial orthonormal k-frames in C. Thus any finite-dimensional representation ρ : U(k) −→ GL(W ) of U(k) gives rise to the natural vector bundle St(k, n)×ρ W −→ G(k, n), where St(k, n) −→ G(k, n) is viewed as ...

We discuss Matijevic–Roberts type theorem on strong F -regularity, F -purity, and Cohen–Macaulay F -injective (CMFI for short) property. Related to this problem, we also discuss the base change problem and the openness of loci of these properties. In particular, we define the notion of F -purity of homomorphisms using Radu–André homomorphisms, and prove basic properties of it. We also discuss a...

Bounds on the range of random graph homomorphism into Z, and the maximal height difference of the Gaussian random field, are presented.

Eilenberg’s variety theorem gives a bijective correspondence between varieties of languages and varieties of finite semigroups. The second author gave a similar relation between conjunctive varieties of languages and varieties of semiring homomorphisms. In this paper, we add a third component to this result by considering varieties of meet automata. We consider three significant classes of lang...

0.1. Endomorphisms of elliptic curves. Recall that a homomorphism of complex elliptic curves is just a holomorphic map E1 → E2 which preserves the origin. (It turns out that this condition is enough to force it to be a homomorphism of groups in the usual sense; why?) An isogeny of elliptic curves is a homomorphism whose kernel is a finite subgroup of E1. In fact the kernel of a homomorphism of ...

We show that a pointwise convergent sequence (n) n2IN of continuous collineations of a compact projective plane converges uniformly if and only if the pointwise limit of (n) n2IN has a quadrangle in its image. Moreover is then a continuous collineation. Furthermore, we derive that a homomorphism between topological projective planes is continuous if and only if it is continuous at some point.

In this paper we prove the Schur-Weyl duality between the symplectic group and the Brauer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer algebra Bn(−2m) to the endomorphism algebra of the tensor space (K2m)⊗n as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is always surj...

1 Let K be a field, V a finite-dimensional vector space over K, and T ∈ EndK(V ). For k ∈ K and S ∈ EndK(V ), define kS : V → V, v → k S(v). (a) Let Φ : K[x] → EndK(V ) be defined by Φ(k0 + k1x + k2x + . . . + knx) = k0T 0 + k1T 1 + k2T 2 + . . . + knT, where T 0 = idV . This is well-defined because a polynomial is completely determined by its coefficients. We will show that this is a homomorph...