The paper studies the class of commutative medial ternary groupoids. A construction of ternary semiterms is given and it is
proved that the equational theory of medial commutative ternary groupoids is solvable, namely, an algorithm is found, which
in allmedial commutative ternary groupoids verifies the validity of the identity u = v for any pair (u, v) of terms. A construction of free medial commutative ternary groupoids is given, and it is proved that anymedial commutative
ternary groupoid has a convex linear representation. 相似文献
In this paper we characterize those bounded linear transformations Tf carrying L1(ℝ1) into the space of bounded continuous functions on ℝ1, for which the convolution identity T(f * g) = Tf · Tg holds. It is shown that such a transformation is just the Fourier transform combined with an appropriate change of variable. 相似文献
We introduce degree n Sabinin algebras, which are defined by the polynomial identities up to degree n in a Sabinin algebra. Degree 4 Sabinin algebras can be characterized by the polynomial identities satisfied by the commutator, associator, and two quaternators in the free nonassociative algebra. We consider these operations in a free power associative algebra and show that one of the quaternators is redundant. The resulting algebras provide the natural structure on the tangent space at the identity element of an analytic loop for which all local loops satisfy monoassociativity, a2a ≡ aa2. These algebras are the next step beyond Lie, Malcev, and Bol algebras. We also present an identity of degree 5 which is satisfied by these three operations but which is not implied by the identities of lower degree. 相似文献
We use computer algebra to determine all the multilinear polynomial identities of degree ≤7 satisfied by the trilinear operations (a·b)·c and a·(b·c) in the free dendriform dialgebra, where a·b is the pre-Lie or the pre-Jordan product. For the pre-Lie triple products, we obtain one identity in degree 3, and three independent identities in degree 5, and we show that every identity in degree 7 follows from the identities of lower degree. For the pre-Jordan triple products, there are no identities in degree 3, five independent identities in degree 5, and ten independent irreducible identities in degree 7. Our methods involve linear algebra on large matrices over finite fields, and the representation theory of the symmetric group. 相似文献
Let |·| be a fixed absolute norm onR2. We introduce semi-|·|-summands (resp. |·|-summands) as a natural extension of semi-L-summands (resp.L-summands). We prove that the following statements are equivalent. (i) Every semi-|·|-summand is a |·|-summand, (ii) (1, 0)
is not a vertex of the closed unit ball ofR2 with the norm |·|. In particular semi-Lp-summands areLp-summands whenever 1<p≦∞. The concept of semi-|·|-ideal (resp. |·|-ideal) is introduced in order to extend the one of semi-M-ideal (resp.M-ideal). The following statements are shown to be equivalent. (i) Every semi-|·|-ideal is a |·|-ideal, (ii) every |·|-ideal
is a |·|-summand, (iii) (0, 1) is an extreme point of the closed unit ball ofR2 with the norm |·|. From semi-|·|-ideals we define semi-|·|-idealoids in the same way as semi-|·|-ideals arise from semi-|·|-summands.
Proper semi-|·|-idealoids are those which are neither semi-|·|-summands nor semi-|·|-ideals. We prove that there is a proper
semi-|·|-idealoid if and only if (1, 0) is a vertex and (0, 1) is not an extreme point of the closed unit ball ofR2 with the norm |·|. So there are no proper semi-Lp-idealoids. The paper concludes by showing thatw*-closed semi-|·|-idealoids in a dual Banach space are semi-|·|-summands, so no new concept appears by predualization of semi-|·|-idealoids. 相似文献
Slim groupoids are groupoids satisfying x(yz) ≈ xz. We find all simple slim groupoids and all minimal varieties of slim groupoids. Every slim groupoid can be embedded into
a subdirectly irreducible slim groupoid. The variety of slim groupoids has the finite embeddability property, so that the
word problem is solvable. We introduce the notion of a strongly nonfinitely based slim groupoid (such groupoids are inherently
nonfinitely based) and find all strongly nonfinitely based slim groupoids with at most four elements; up to isomorphism, there
are just two such groupoids.
The work is a part of the research project MSM0021620839 financed by MSMT. 相似文献
It is proved that any lattice-ordered pregroup that satisfies an identity of the form xll···l = xrr···r (for the same number of l,r-operations on each side) has a lattice reduct that is distributive. It follows that every such ?-pregroup is embedded in an ?-pregroup of residuated and dually residuated maps on a chain. 相似文献
Let K be a simply-connected compact Lie Group equipped with an AdK-invariant inner product on the Lie Algebra ?, of K. Given this data, there is a well known left invariant “H1-Riemannian structure” on L(K) (the infinite dimensional group of continuous based loops in K), as well as a heat kernel νT(k0, ·) associated with the Laplace-Beltrami operator on L(K). Here T > 0, k0∈L(K), and νT (k0, ·) is a certain probability measure on L(K). In this paper we show that ν1(e,·) is equivalent to Pinned Wiener Measure on K on ?s0≡<xt: t∈ [0, s0]> (the σ-algebra generated by truncated loops up to “time”s0).
Recevied: 9 September 1999 / Revised version: 13 March 2000 / Published online: 22 November 2000 相似文献
In this work, we investigate some groupoids that are Abelian algebras and Hamiltonian algebras. An algebra is Abelian if for
every polynomial operation and for all elements a, b, [`(c)] \bar{c} , [`(d)] \bar{d} the implication t( a,[`(c)] ) = t( a,[`(d)] ) T t( b,[`(c)] ) = t( b,[`(d)] ) t\left( {a,\bar{c}} \right) = t\left( {a,\bar{d}} \right) \Rightarrow t\left( {b,\bar{c}} \right) = t\left( {b,\bar{d}} \right) holds. An algebra is Hamiltonian if every subalgebra is a block of some congruence on the algebra. R. J. Warne in 1994 described
the structure of the Abelian semigroups. In this work, we describe the Abelian groupoids with identity, the Abelian finite
quasigroups, and the Abelian semigroups S such that abS = aS and Sba = Sa for all a, b ∈ S. We prove that a finite Abelian quasigroup is a Hamiltonian algebra. We characterize the Hamiltonian groupoids with identity
and semigroups under the condition of Abelianity of these algebras. 相似文献
Let M^n be a smooth, compact manifold without boundary, and F0 : M^n→ R^n+1 a smooth immersion which is convex. The one-parameter families F(·, t) : M^n× [0, T) → R^n+1 of hypersurfaces Mt^n= F(·,t)(M^n) satisfy an initial value problem dF/dt (·,t) = -H^k(· ,t)v(· ,t), F(· ,0) = F0(· ), where H is the mean curvature and u(·,t) is the outer unit normal at F(·, t), such that -Hu = H is the mean curvature vector, and k 〉 0 is a constant. This problem is called H^k-fiow. Such flow will develop singularities after finite time. According to the blow-up rate of the square norm of the second fundamental forms, the authors analyze the structure of the rescaled limit by classifying the singularities as two types, i.e., Type Ⅰ and Type Ⅱ. It is proved that for Type Ⅰ singularity, the limiting hypersurface satisfies an elliptic equation; for Type Ⅱ singularity, the limiting hypersurface must be a translating soliton. 相似文献
We give sufficient conditions for a differential equation to have a given semisimple group as its Galois group. For any group G with G0 = G1 · ··· · Gr, where each Gi is a simple group of type A?, C?, D?, E6, or E7, we construct a differential equation over C(x) having Galois group G. 相似文献
Let M be a connected complex manifold endowed with a Hermitian metric g. In this paper, the complex horizontal and vertical Laplacians associated with the induced Hermitian metric 〈·, ·〉 on the
holomorphic tangent bundle T1,0M of M are defined, and their explicit expressions are obtained. Using the complex horizontal and vertical Laplacians associated
with the Hermitian metric 〈·, ·〉 on T1,0M, we obtain a vanishing theorem of holomorphic horizontal p forms which are compactly supported in T1,0M under the condition that g is a Kaehler metric on M. 相似文献
The Dirichlet problem for elliptic systems of the second order with constant real and complex coefficients in the half-space k+ = {x = (x1,…,xk): xk > 0} is considered. It is assumed that the boundary values of a solution u = (u1,…,um) have the form ψ1ξ1 + · · · + ψnξn, 1 ≤ n ≤ m, where ξ1,· · ·,ξn is an orthogonal system of m-component normed vectors and ψ1,· · ·,ψn are continuous and bounded functions on ?k+. We study the mappings [C(?k+)]n ? (ψ1,…,ψn) → u(x) ? m and [C(?k+)]n ? (ψ1,…,ψn) → u(x) ? m generated by real and complex vector valued double layer potentials. We obtain representations for the sharp constants in inequalities between |u(x)| or |(z, u(x))| and ∥u|xk=0∥, where z is a fixed unit m-component vector, | · | is the length of a vector in a finite-dimensional unitary space or in Euclidean space, and (·,·) is the inner product in the same space. Explicit representations of these sharp constants for the Stokes and Lamé systems are given. We show, in particular, that if the velocity vector (the elastic displacement vector) is parallel to a constant vector at the boundary of a half-space and if the modulus of the boundary data does not exceed 1, then the velocity vector (the elastic displacement vector) is majorised by 1 at an arbitrary point of the half-space. An analogous classical maximum modulus principle is obtained for two components of the stress tensor of the planar deformed state as well as for the gradient of a biharmonic function in a half-plane. 相似文献
Let (m, n) ∈ ℕ2, Ω an open bounded domain in ℝm, Y = [0, 1]m; uε in (L2(Ω))n which is two-scale converges to some u in (L2(Ω × Y))n. Let φ: Ω × ℝm × ℝn → ℝ such that: φ(x, ·, ·) is continuous a.e. x ∈ Ω φ(·, y, z) is measurable for all (y, z) in ℝm × ℝn, φ(x, ·, z) is 1-periodic in y, φ(x, y, ·) is convex in z. Assume that there exist a constant C1 > 0 and a function C2 ∈ L2(Ω) such that
In the note we consider ordered groupoids with the Riesz interpolation property, that is, ifai≤bj (i, j=1,2), then there exists ac such thatai≤c≤bj (i, j=1,2). For such groupoids possessing the descending chain condition for the positive cone and the property
a theorem analogous to the fundamental theorem of arithmetic is proved. The result is a generalization of known results for
lattice-ordered monoids, loops, and quasigroups.
Translated fromMatematicheskie Zametki, Vol. 62, No. 6, pp. 910–915, December, 1997.
Translated by A. I. Shtern 相似文献
In an earlier paper [E4] we introduced an algebraic structure on sets of homotopy classes [Sp ×Sq;Sn], given by the reflecting product on spheresSn, which makes these sets symmetric groupoids. In this article we determine precisely the algebraic structure of the symmetric groupoids ([Sn ×Sn;Sn], ) forn 1, 3, 7. 相似文献
Let s ∈ {2.3,…} and E be an Archimedean vector lattice. We prove that there exists a unique pair (E?,?), where E? is an Archimedean vector lattice and ?:E× ··· ×E (s times) → E? is a symmetric lattice s-morphism, such that for every Archimedean vector lattice F and every symmetric lattice s-morphism T:E × ··· × E (s times) → F, there exists a unique lattice homomorphism T?:E? → F such that T = T?○?. We give two approaches to construct (E?,?) based on f-algebras and functional calculus, respectively, provided that E is also uniformly complete. 相似文献