Graduate Studies in Mathematics(共212册),这套丛书还有 《Cartan for Beginners》《Embeddings in Manifolds》《Organized Collapse: An Introduction to Discrete Morse Theory》《Algebraic Curves and Riemann Surfaces (Graduate Studies in Mathematics, Vol 5)》《Elements of Combinatorial And Differential Topology》...
Let $G={m Spec} A$ be a linearly reductive group and let $w_G\\\in A^*$ be the invariant integral on $G$. We establish the harmonic analysis on $G$ and we compute $w_G$ when $G=Sl_n, Gl_n, O_n, Sp_{2n}$ by geometric arguments and by means of the Fourier transform...
In most institutions it is either a service course for analysts, on abstract spaces, or else an introduction to homological algebra in which the only geometric activity is the completion of commutative diagrams. Pictures are kept to a minimum, and at the end the student still does nr~ ...
SYMPLECTIC groupsSTRING theoryALGEBRAMATHEMATICAL modelsWe introduce a new class of representations of the cohomological Hall algebras of Kontsevich and Soibelman which we call cohomological Hall modules, or CoHM for short. These representations are constructed from self-dual representations of a quiver ...
From this perspective, the existence of (pseudo- )Riemannian metrics for simple Lie groups and algebras is an accident. Not only does the geometry of symplectic groupoids underlay the kinematics of point particles, but it also provides a geometric framework for formulating Poisson electrody- ...
Information on L-algebras, their structure groups and applications, can be drawn from [62], [63], [67], [68], [70]. For a very brief introduction, see Section 1. We will show that there are simple conditions which specialize an L-algebra to the three above mentioned systems of non-...
Vector Space and Linear Maps | Tensor Algebra | Skew-symmetric Tensors and Exterior Algebra | Euclidean and Symplectic Vector Spaces | Duality and Euclidean Tensors | Differentiable Manifolds | One-Parameter Groups of Diffeomorphisms | Exterior Derivative and Integration | Absolute Differential Calculus ...
Crossed Product Algebras and the Homology of Certain p-Adic and Adélic Dynamical Systems We identify the Hochschild, cyclic, and periodic cyclic homology groups of dynamical systems algebras arising from the action of Q on the spaces of finite ... LV Nistor - K-Theory 被引量: 15发表: 2000...
This book systematically develops purely mathematical applications of geometric algebra useful in physics, including extensive applications to linear algebra and transformation groups. It contains sufficient material for a course on mathematical topics alone. The second edition has been expanded by nearly a...
Despite its success,there were problems with the geocentric (earth-centered) cosmology.In the most general sense,astronomical observations did not squarely agree with the mathematics.And,these were simple geometric calculations about circular orbits not some mystical higher mathematics.As mentioned above,...