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Related to Algebras: Operator algebras, Lie algebras
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In this way I believed that I could borrow all that was best both in geometrical analysis and in algebra, and correct all the defects of the one by help of the other.
"Well, algebra is a tool, like the plow or the hammer, and a good tool to those who know how to use it."
"First effects of algebra," replied Barbicane; "and now, to finish, we are going to prove the given number of these different expressions, that is, work out their value."
You shall try and make me like algebra, and I 'll try and make you like Latin, will you?"
Orthography, etymology, syntax, and prosody, biography, astronomy, geography, and general cosmography, the sciences of compound proportion, algebra, land-surveying and levelling, vocal music, and drawing from models, were all at the ends of his ten chilled fingers.
"I can't stop to measure insteps on algebra days; I've noticed your habit of keeping a foot in the aisle ever since you had those new shoes, so I don't wonder it was stepped on."
Helen Plantagenet is deeply grieved to have to confess that I took the first place in algebra yesterday unfairly.
He himself undertook his daughter's education, and to develop these two cardinal virtues in her gave her lessons in algebra and geometry till she was twenty, and arranged her life so that her whole time was occupied.
In the boys' department, which was full of little urchins (varying in their ages, I should say, from six years old to ten or twelve), the master offered to institute an extemporary examination of the pupils in algebra; a proposal, which, as I was by no means confident of my ability to detect mistakes in that science, I declined with some alarm.
Following a conjecture of Enomoto and Kashiwara in [EK06] concerning categories of modules over affine Hecke algebras of type B, proved in general by Varagnolo and Vasserot [VV11], Kashiwara and Miemietz conjectured analogous results for type D affine Hecke algebras, see [KM07].
Lts constitute examples of ternary algebras. If (g, [,]) is a Lie algebra, then (g, [,,]) is a Lts, where [x, y, z] := [[x, y], z] (see [1, 4, 5]).
Finite-dimensional Hopf algebras H have an elusive nature.
We introduced a new nonassociative and noncommutative algebra which has several properties similar to nonassociative and commutative algebras.
In symmetric geometry, the study of symplectic algebras is important in manifolds because of the structure of the symplectic group SP(2n, R) preserving the transformations of the symplectic vector space at any point of symplectic manifolds, and the reader is kindly requested to refer to [7] to get more applications and interactions with classical mechanics.