algebra|algebras in English

noun

[al·ge·bra || 'ældʒɪbrə]

mathematical system that uses equations containing letters and numbers

Use "algebra|algebras" in a sentence

1. Cluster Algebras homological algebra quivers representation theory triangulated categories

2. Similarly, one may look for deformations of a zinbiel algebra into dendriform Algebras, and wonder

3. Although the theory of Lie Algebras doesn’t require an algebraic closed scalar field – and many real Lie Algebras are important – it is more than convenient as soon as a Lie algebra is a matrix algebra, i.e

4. In operator algebra, the Koecher–Vinberg theorem is a reconstruction theorem for real Jordan algebras.

5. His 1935 paper, "On the Structure of Abstract Algebras" founded a new branch of mathematics, universal algebra.

6. Algebras, Quivers and Representations is targeted at researchers and graduate students in algebra, representation theory and triangulated categories

7. Kim [15] introduced a new notion, called a BH-algebra, which is a generalization of BCH / BCI / BCK-Algebras.

8. He has made contributions to the fields of probability and algebra, especially semisimple Lie groups, Lie algebras, and Markov processes.

9. Tive Algebras, Jordan Algebras, alternative Algebras, composition Algebras, Hopf Algebras, and Lie Algebrasthese last being the primary focus of our study

10. He deals with modular representation theory of finite groups and related questions of algebraic topology, representation theory of finite algebras and homologous algebra.

11. Clifford algebras are closely related to exterior algebras.

12. The best-known examples of Algebras are Algebras of square matrices, Algebras of polynomials and Algebras of formal power series over fields

13. These algebras form a generalization of finite-dimensional semisimple Lie algebras, and many properties related to the structure of a Lie algebra such as its root system, irreducible representations, and connection to flag manifolds have natural analogues in the Kac–Moody setting.

14. Matrix addition and multiplication make the set of all n × n matrices into an associative algebra and hence there is a corresponding representation theory of associative algebras.

15. Kac-Moody algebras!

16. In pure mathematics, quaternions show up significantly as one of the four finite-dimensional normed division algebras over the real numbers, with applications throughout algebra and geometry.

17. Algebra and Number Theory; Linear Algebra

18. Hochschild (1945) introduced Hochschild cohomology, a cohomology theory for algebras, which classifies deformations of algebras.

19. Araki works on axiomatic quantum field theory and statistical mechanics in particular on application of operator algebras (von Neumann algebras, C*-algebras).

20. Incidence algebras of locally finite partially ordered sets are associative algebras considered in combinatorics.

21. A boolean algebra is FREE on the set of generators S iff any map from S to any boolean algebra extends to a unique boolean homomorphism (that is, viewing boolean Algebras as one-object division allegories, it extends to a representation of division allegories).

22. The author also discusses CCR Algebras, but he calls them "liminal" Algebras

23. In a strict sense, the theory of Algebras (in particular, noncommutative Algebras) originated fromasingleexample, namelythequaternions, createdbySirWilliamR.Hamilton in1843.

24. What are synonyms for Algebras?

25. All associative algebras are alternative.