نتایج جستجو برای: exceptional simple group
تعداد نتایج: 1417326 فیلتر نتایج به سال:
Understanding the genetic mechanisms of sensitivity to targeted anticancer therapies may improve patient selection, response to therapy, and rational treatment designs. One approach to increase this understanding involves detailed studies of exceptional responders: rare patients with unexpected exquisite sensitivity or durable responses to therapy. We identified an exceptional responder in a ph...
We prove that for a simple simply connected quasi-split group of type 3,6D4, E6, E7 defined over a perfect field F of characteristic 6= 2, 3 the Rost invariant has trivial kernel. In certain cases we give a formula for the Rost invariant. It follows immediately from the result above that if cdF ≤ 2 (resp. vcdF ≤ 2) then Serre’s Conjecture II (resp. the Hasse principle) holds for such a group. F...
Suppose that is a finite group. Then the set of all prime divisors of is denoted by and the set of element orders of is denoted by . Suppose that . Then the number of elements of order in is denoted by and the sizes of the set of elements with the same order is denoted by ; that is, . In this paper, we prove that if is a group such that , where , then . Here denotes the family of Suzuk...
In this paper, we consider the connected split rank one Lie group of real type F4 which we denote by F4. We first exhibit F4 as a group of operators on the complexification of A. A. Albert's exceptional simple Jordan algebra. This enables us to explicitly realize the symmetric space F4/Spin(9) as the unit ball in R with boundary S . After decomposing the space of spherical harmonics under the a...
Let G be an exceptional Lie group with T ⊂ G a maximal torus. We express the integral cohomology ring H(G/T ) by a minimal set of Schubert classes on G/T . This completes the program of determining the integral cohomology of all complete flag manifolds G/T in the context of Schubert calculus. The results are used in [DZ3] to construct the integral cohomology of a simple Lie group G in terms of ...
We give an explicit construction of the simply-connected compact real form of the Lie group of type E7, as a group of 28 × 28 matrices over quaternions, acting on a 28-dimensional left quaternion vector space. This leads to a description of the simply-connected split real form, acting on a 56dimensional real vector space, and thence to the finite quasi-simple groups of type E7. The sign problem...
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