摘要: For a Lie algebra over a ring, the lattice of cosets is constructed. Necessary and sufficient conditions for the distributivity, modularity, and semimodularity of coset lattices are found. The fundamental theorem of affine geometry for nilpotent Lie algebras of class 2 is proved....
Affine map and new affine system. If the viare linearly dependent, the map is degenerated. In particular, if ηd +1 = … = ηn = 0 for all x, the map creates an axonometric image as used in descriptive geometry. Simple examples are the so-called cavalier and military projections, ...
Algebra, Arithmetic and Geometry with Applications || Geometric Applications of the Residue Theorem on Algebraic Curves We identify a class of weighted complete intersection Calabi-Yau manifolds with Gepner models involving the non-diagonal invariants. To this end we extend ... C Christensen,A Sathaye...
We prove that $QH^*_{\\mathrm{aff}}(G/B)$ is a Frobenius algebra, and that the new quantum product determines a flat Dubrovin connection. We further develop an analogue of Givental and Kim formalism for this ring and we deduce a presentation of $QH^*_{\\mathrm{aff}}(G/B)$ by ...
Elekes, Sums versus products in number theory, al- gebra and Erd˝os geometry, manuscript, 2001... G Elekes 被引量: 146发表: 0年 Traces in strict Frobenius algebras and strict complete intersections. Bezout's theorem. 2. The Cayley-Bacharach theorem. 3. A formula of Jacobi related to ...
Kowalski, E.: The Large Sieve and Its Applications. Arithmetic Geometry, Random Walks and Discrete Groups. Cambridge Tracts in Mathematics, vol. 175. Cambridge University Press, Cambridge (2008) MATH Google Scholar Lang, S.: Algebra, 3rd edn. Springer, New York (2002) MATH Google Scholar...
Mathematics - Algebraic GeometryWe construct the affine version of the Fomin-Kirillov algebra, called the affine FK algebra, to investigate the combinatorics of affine Schubert calculus for type $A$. We introduce Murnaghan-Nakayama elements and Dunkl elements in the affine FK algebra. We show that...
group S and an ideal I of it, we provide two different approaches in order to check whether S ∖ I is finite and, if so, to compute its elements: the first one uses similar procedures to those suggested for C -cofinite submonoids, the second one uses tools from commutative algebra....