Results 251 to 260 of about 10,393,784 (287)
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The Order of the Antipode of a Finite Dimensional Hopf Algebra is Finite
American Journal of Mathematics, 1976Let A be a finite dimensional Hopf algebra over a field k with antipode s. For a nonzero left integral x in A let a E G (A*) = Alg(A, k) satisfy xh = a(h)x for all h EA, and let a E G (A) be the corresponding element for A*. Then s4(h)=a-'(a -ha-')a. From this we prove the main result of the paper: the order of the antipode of a finite dimensional Hopf
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1992
An element P of any group is said to have order m if $$\displaystyle{mP =\mathop{\underbrace{ P + P + \cdots + P}}\limits _{\mbox{ $m$ summands}} = \mathcal{O},}$$ but \(m'P\neq \mathcal{O}\) for all integers 1 ≤ m′ < m. If such an m exists, then P has finite order, otherwise it has infinite order. We begin our study of points of finite order on
Joseph H. Silverman, John T. Tate
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An element P of any group is said to have order m if $$\displaystyle{mP =\mathop{\underbrace{ P + P + \cdots + P}}\limits _{\mbox{ $m$ summands}} = \mathcal{O},}$$ but \(m'P\neq \mathcal{O}\) for all integers 1 ≤ m′ < m. If such an m exists, then P has finite order, otherwise it has infinite order. We begin our study of points of finite order on
Joseph H. Silverman, John T. Tate
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1993
The purpose of this chapter is to develop a general framework for the theory of geometric objects and operators and to reduce local geometric considerations to finite order problems. In general, the latter is a hard analytical problem and its solution essentially depends on the category in question.
Ivan Kolář +2 more
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The purpose of this chapter is to develop a general framework for the theory of geometric objects and operators and to reduce local geometric considerations to finite order problems. In general, the latter is a hard analytical problem and its solution essentially depends on the category in question.
Ivan Kolář +2 more
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1998
When remote sensing of the atmosphere is performed at wavelengths whose optical thickness is small or when the albedo for single scattering is small, then reflected, transmitted, and internal intensities can be computed through an approximate method which enumerates the intensity fields up to a finite number of scatterings.
Harriet H. Natsuyama +2 more
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When remote sensing of the atmosphere is performed at wavelengths whose optical thickness is small or when the albedo for single scattering is small, then reflected, transmitted, and internal intensities can be computed through an approximate method which enumerates the intensity fields up to a finite number of scatterings.
Harriet H. Natsuyama +2 more
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Intermittent control for finite-time synchronization of fractional-order complex networks
Neural Networks, 2021Lingzhong Zhang +2 more
exaly
Low-Order Preconditioning for the High-Order Finite Element de Rham Complex
SIAM Journal of Scientific Computing, 2023Tzanio Kolev, Will Pazner
exaly