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We establish a multiplication formula for a tridiagonal standard basis element in the idempotent version, i.e., the Lusztig form, of the coideal subalgebras of quantum affine arising from the geometry of affine partial flag varieties of type C. We apply this formula to obtain the stabilization algebras , , and , which are idempotented coideal subalgebras of quantum affine . The symmetry in the formula leads to an isomorphism of the idempotented coideal subalgebras and with compatible monomial, standard and canonical bases. 相似文献
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Steven Hoehner 《Journal of Mathematical Analysis and Applications》2022,505(2):125506
For a convex body K in , we introduce and study the extremal general affine surface areas, defined by where and are the and affine surface area of K, respectively. We prove that there exist extremal convex bodies that achieve the supremum and infimum, and that the functionals and are continuous. In our main results, we prove Blaschke-Santaló type inequalities and inverse Santaló type inequalities for the extremal general affine surface areas. This article may be regarded as an Orlicz extension of the recent work of Giladi, Huang, Schütt and Werner (2020), who introduced and studied the extremal affine surface areas. 相似文献
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Masoumah Al-Ali 《Journal of Pure and Applied Algebra》2019,223(12):5430-5443
Let be a simple, finite-dimensional complex Lie algebra, and let denote the universal affine vertex algebra associated to at level k. The Cartan involution on lifts to an involution on , and we denote by the orbifold, or fixed-point subalgebra, under this involution. Our main result is an explicit minimal strong finite generating set for for generic values of k. 相似文献
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《Expositiones Mathematicae》2022,40(4):845-869
We make several observations relating the Lie algebra , associative 3-planes, and subalgebras. Some are likely well-known but not easy to find in the literature, while other results are new. We show that an element cannot have rank 2, and if it has rank 4 then its kernel is an associative subspace. We prove a canonical form theorem for elements of . Given an associative 3-plane in , we construct a Lie subalgebra of that is isomorphic to . This subalgebra differs from other known constructions of subalgebras of determined by an associative 3-plane. These are results of an NSERC undergraduate research project. The paper is written so as to be accessible to a wide audience. 相似文献
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Becky Armstrong Lisa Orloff Clark Kristin Courtney Ying-Fen Lin Kathryn McCormick Jacqui Ramagge 《Journal of Pure and Applied Algebra》2022,226(3):106853
We introduce twisted Steinberg algebras over a commutative unital ring R. These generalise Steinberg algebras and are a purely algebraic analogue of Renault's twisted groupoid C*-algebras. In particular, for each ample Hausdorff groupoid G and each locally constant 2-cocycle σ on G taking values in the units , we study the algebra consisting of locally constant compactly supported R-valued functions on G, with convolution and involution “twisted” by σ. We also introduce a “discretised” analogue of a twist Σ over a Hausdorff étale groupoid G, and we show that there is a one-to-one correspondence between locally constant 2-cocycles on G and discrete twists over G admitting a continuous global section. Given a discrete twist Σ arising from a locally constant 2-cocycle σ on an ample Hausdorff groupoid G, we construct an associated twisted Steinberg algebra , and we show that it coincides with . Given any discrete field , we prove a graded uniqueness theorem for , and under the additional hypothesis that G is effective, we prove a Cuntz–Krieger uniqueness theorem and show that simplicity of is equivalent to minimality of G. 相似文献
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In this paper, we establish a complete classification of locally strongly convex isotropic centroaffine hypersurfaces in the -dimensional affine space . 相似文献
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In this note, with a purely geometric approach, the covering radius of the group is determined. Also, a new proof establishing the covering radii of and is provided. 相似文献