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91.
This is a survey of some recent results on spherical tropical geometry. 相似文献
92.
Standard Embeddings of Smooth Schubert Varieties in Rational Homogeneous Manifolds of Picard Number 1 下载免费PDF全文
Smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 are horospherical varieties. We characterize standard embeddings of smooth Schubert varieties in rational homogeneous manifolds of Picard number 1 by means of varieties of minimal rational tangents. In particular, we mainly consider nonhomogeneous smooth Schubert varieties in symplectic Grassmannians and in the 20-dimensional F_4- homogeneous manifold associated to a short simple root. 相似文献
93.
94.
By using the Ringel-Hall algebra approach, we investigate the structure of the Lie algebra L(A) generated by indecomposable constructible sets in the varieties of modules for any finite- dimensional C-algebra A. We obtain a geometric realization of the universal enveloping algebra R(A) of L(A), this generalizes the main result of Riedtmann. We also obtain Green's formula in a geometric form for any finite-dimensional C-algebra A and use it to give the comultiplication formula in R(A). 相似文献
95.
Letitia Golubitsky 《代数通讯》2013,41(6):2091-2105
It is well known that the Eulerian polynomials, which count permutations in S n by their number of descents, give the h-polynomial/h-vector of the simple polytopes known as permutohedra, the convex hull of the S n -orbit for a generic weight in the weight lattice of S n . Therefore, the Eulerian polynomials give the Betti numbers for certain smooth toric varieties associated with the permutohedra. In this article we derive recurrences for the h-vectors of a family of polytopes generalizing this. The simple polytopes we consider arise as the orbit of a nongeneric weight, namely, a weight fixed by only the simple reflections J = {s n , s n?1, s n?2,…, s n?k+2, s n?k+1} for some k with respect to the A n root lattice. Furthermore, they give rise to certain rationally smooth toric varieties X(J) that come naturally from the theory of algebraic monoids. Using effectively the theory of reductive algebraic monoids and the combinatorics of simple polytopes, we obtain a recurrence formula for the Poincaré polynomial of X(J) in terms of the Eulerian polynomials. 相似文献
96.
Harlan Kadish 《代数通讯》2013,41(5):2171-2180
97.
98.
S. K. Pattanayak 《代数通讯》2013,41(9):3811-3822
For any simple, simply connected algebraic group G of exceptional types (E 6, E 7, E 8, F 4, and G 2) and for any maximal parabolic subgroup P of G, we describe all minimal (with respect to inclusion) Schubert varieties in G/P admitting semistable points for the action of a maximal torus T with respect to an ample line bundle on G/P. This completes the answer to a question proposed in [8] and settled there in the classical case. 相似文献
99.
Alexey Kuz'min 《代数通讯》2013,41(8):3169-3189
Since 1976, it is known from the paper by V. P. Belkin that the variety RA2 of right alternative metabelian (solvable of index 2) algebras over an arbitrary field is not Spechtian (contains nonfinitely based subvarieties). In 2005, S. V. Pchelintsev proved that the variety generated by the Grassmann RA2-algebra of finite rank r over a field ?, for char(?) ≠ 2, is Spechtian iff r = 1. We construct a nonfinitely based variety 𝔐 generated by the Grassmann 𝒱-algebra of rank 2 of certain finitely based subvariety 𝒱 ? RA2 over a field ?, for char(?) ≠ 2, 3, such that 𝔐 can also be generated by the Grassmann envelope of a five-dimensional superalgebra with one-dimensional even part. 相似文献
100.