Maps Between Deformed and Ordinary Gauge Fields

In this paper, we introduce a map between the q-deformed gauge fields defined on the GL_q(N) -covariant quantum hyperplane and the ordinary gauge fields. Perturbative analysis of the q-deformed QED at the classical level is presented and gauge fixing à la BRST is discussed. Another star product defined on the hybrid (q,h) -plane is explicitly constructed.     

Flow prolongation of some tangent valued forms

We study the prolongation of semibasic projectable tangent valued k-forms on fibered manifolds with respect to a bundle functor F on local isomorphisms that is based on the flow prolongation of vector fields and uses an auxiliary linear r-th order connection on the base manifold, where r is the base order of F. We find a general condition under which the Frölicher-Nijenhuis bracket is preserved. Special attention is paid to the curvature of connections. The first order jet functor and the tangent functor are discussed in detail. Next we clarify how this prolongation procedure can be extended to arbitrary projectable tangent valued k-forms in the case F is a fiber product preserving bundle functor on the category of fibered manifolds with m-dimensional bases and local diffeomorphisms as base maps.     

Smash Products for Secondary Homotopy Groups

We construct a smash product operation on secondary homotopy groups yielding the structure of a lax symmetric monoidal functor. Applications on cup-one products, Toda brackets and Whitehead products are considered. The second author was partially supported by the Spanish Ministry of Education and Science under MEC-FEDER grants MTM2004-01865 and MTM2004-03629, the postdoctoral fellowship EX2004-0616, and a Juan de la Cierva research contract.     

Dendriform equations

We investigate solutions for a particular class of linear equations in dendriform algebras. Motivations as well as several applications are provided. The latter follow naturally from the intimate link between dendriform algebras and Rota–Baxter operators, e.g. the Riemann integral map or Jackson's q-integral.     

The Hamiltonian Structures of 3D ODE with Time-Independent Invariants

ＴＨＥＨＡＭＩＬＴＯＮＩＡＮＳＴＢＵＣＴＵＲＥＳＯＦ３ＤＯＤＥＷＩＴＨＴＩＭＥ－ＩＮＤＥＰＥＮＤＥＮＴＩＮＶＡＲＩＡＮＴＳＧｕｏＺｈｏｎｇ－ｈｅｎｇ（郭仲衡）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊ...     

新型Poisson括号意义下的无穷维Lie代数

本文首先针对ＫｄＶ方程的Ｈａｍｉｌｔｏｎ形式，建立一种比较容易验证的新型Ｐｏｉｓｓｏｎ括号和无穷维Ｌｉｅ代数．其次，研究ＫｄＶ方程的Ｈａｍｉｌｔｏｎ形式的第一积分与新型Ｐｏｉｓｏｎ括号的关系，得到判定第一积分的充分必要条件．最后，构造ＫｄＶ方程的第一积分．     

Topological quantum field theory with corners based on the Kauffman bracket

We describe the construction of a topological quantum field theory with corners based on the Kauffman bracket, that underlies the smooth theory of Lickorish, Blanchet, Habegger, Masbaum and Vogel. We also exhibit some properties of invariants of 3-manifolds with boundary. Received: March 4, 1996     

Homomorphic images and rationalizations based on the Eilenberg-Maclane spaces

Are there any kinds of self maps on the loop structure whose induced homomorphic images are the Lie brackets in tensor algebra? We will give an answer to this question by defining a self map of ΩΣK(\(\mathbb{Z}\), 2d), and then by computing efficiently some self maps. We also study the topological rationalization properties of the suspension of the Eilenberg-MacLane spaces. These results will be playing a powerful role in the computation of the same n-type problems and giving us an information about the rational homotopy equivalence.     

On the calculation of the Kauffman bracket polynomial

In this paper, we present a new algorithm to evaluate the Kauffman bracket polynomial. The algorithm uses cyclic permutations to count the number of states obtained by the application of ‘A’ and ‘B’ type smoothings to the each crossing of the knot. We show that our algorithm can be implemented easily by computer programming.