Algebraic Geometry Commons^™

Existence Of Solutions Of The Classical Yang-Baxter Equation For A Real Lie Algebra, Jorg Feldvoss

University Faculty and Staff Publications

We characterize finite-dimensional Lie algebras over the real numbers for which the classical Yang-Baxter equation has a non-trivial skew-symmetric solution (resp. a non-trivial solution with invariant symmetric part). Equivalently, we obtain a characterization of those finite-dimensional real Lie algebras which admit a non-trivial (quasi-) triangular Lie bialgebra structure.

Elliptic Functions And Equations Of Modular Curves, Lev A. Borisov, Paul E. Gunnells, Sorin Popescu

Paul Gunnells

Let P≥5 be a prime. We show that the space of weight one Eisenstein series defines an embedding into P(p−3)/2 of the modular curve X1(p) for the congruence group Γ1(p) that is scheme-theoretically cut out by explicit quadratic equations.

Geometric Realization And K-Theoretic Decomposition Of C*-Algebras, Claude Schochet

Mathematics Faculty Research Publications

Suppose that A is a separable C*-algebra and that G∗ is a (graded) subgroup of the ℤ/2-graded group K∗(A). Then there is a natural short exact sequence

0 → G∗ → K∗(A) → K∗(A)/G∗ → 0.

In this note we demonstrate how to geometrically realize this sequence at the level of C*-algebras. As a result, we KK-theoretically decompose A as

0 → A ⊗ [cursive]K → A_ƒ → SA_t → 0

where K∗(A_t) is the torsion subgroup of …

Extended Powers Of Manifolds And The Adams Spectral Sequence, Robert R. Bruner

Mathematics Faculty Research Publications

The extended power construction can be used to create new framed manifolds out of old. We show here how to compute the effect of such operations in the Adams spectral sequence, extending partial results of Milgram and the author. This gives the simplest method of proving that Jones’ 30-manifold has Kervaire invariant one, and allows the construction of manifolds representing Mahowald’s classes η4 and η5, among others.

Identities For The Multiple Polylogarithm Using The Shuffle Operation, Ji Hoon Ryoo

Electronic Theses and Dissertations

At the beginning of my research, I understood the shuffle operation and iterated integrals to make a new proof-method (called a combinatorial method). As a first work, I proved an combinatorial identity 2 using a combinatorial method. While proving it, I got four identities and showed that one of them is equal to an analytic identity 1 which is found at the paper [2] written by David M. Bradley and Doug Bowman. Furthermore, I derived an formula involving nested harmonic sums. Using Maple (a mathematical software), I found a new combinatorial identity 3 and derived two formulas: One is related …