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Mathematics Subject Classification – MSC2020

17-XX

Nonassociative rings and algebras 42458

17-00

General reference works (handbooks, dictionaries, bibliographies, etc.) from nonassociative rings and algebras 9

17-01

Introductory exposition (textbooks, tutorial papers, etc.) from nonassociative rings and algebras 170

17-02

Research exposition (monographs, survey articles) from nonassociative rings and algebras 495

17-03

History of nonassociative rings and algebras [Consider also classification numbers from Section 01-XX] 68

17-04

Software, source code, etc. for problems from nonassociative rings and algebras 126

17-06

Proceedings, conferences, collections, etc. from nonassociative rings and algebras 492

17-08

Computational methods for problems from nonassociative rings and algebras 228

17-11

Research data for problems from nonassociative rings and algebras 0

17Axx

General nonassociative rings 6357

17A01

General theory of nonassociative rings and algebras 187

17A05

Power-associative rings 244

17A15

Noncommutative Jordan algebras 168

17A20

Flexible algebras 154

17A30

Nonassociative algebras satisfying other identities 1254

17A32

Leibniz algebras 536

17A35

Nonassociative division algebras 508

17A36

Automorphisms, derivations, other operators (nonassociative rings and algebras) 437

17A40

Ternary compositions 802

17A42

Other \(n\)-ary compositions \((n \ge 3)\) 338

17A45

Quadratic algebras (but not quadratic Jordan algebras) 139

17A50

Free nonassociative algebras 273

17A60

Structure theory for nonassociative algebras 420

17A61

Gröbner-Shirshov bases in nonassociative algebras 0

17A65

Radical theory (nonassociative rings and algebras) 240

17A70

Superalgebras 1375

17A75

Composition algebras 283

17A80

Valued algebras 69

17A99

None of the above, but in this section 405

17Bxx

Lie algebras and Lie superalgebras {For Lie groups, see 22Exx} 34245

17B01

Identities, free Lie (super)algebras 982

17B05

Structure theory for Lie algebras and superalgebras 1769

17B08

Coadjoint orbits; nilpotent varieties 297

17B10

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) 4486

17B15

Representations of Lie algebras and Lie superalgebras, analytic theory 312

17B20

Simple, semisimple, reductive (super)algebras 3032

17B22

Root systems 472

17B25

Exceptional (super)algebras 429

17B30

Solvable, nilpotent (super)algebras 2311

17B35

Universal enveloping (super)algebras [See also 16S30] 1961

17B37

Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 8036

17B38

Yang-Baxter equations and Rota-Baxter operators 0

17B40

Automorphisms, derivations, other operators for Lie algebras and super algebras 1603

17B45

Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 887

17B50

Modular Lie (super)algebras 1376

17B55

Homological methods in Lie (super)algebras 877

17B56

Cohomology of Lie (super)algebras 1815

17B60

Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 1062

17B61

Hom-Lie and related algebras 1

17B62

Lie bialgebras; Lie coalgebras 403

17B63

Poisson algebras 749

17B65

Infinite-dimensional Lie (super)algebras [See also 22E65] 2493

17B66

Lie algebras of vector fields and related (super) algebras 1055

17B67

Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 3122

17B68

Virasoro and related algebras 1856

17B69

Vertex operators; vertex operator algebras and related structures 1718

17B70

Graded Lie (super)algebras 1967

17B75

Color Lie (super)algebras 130

17B80

Applications of Lie algebras and superalgebras to integrable systems 669

17B81

Applications of Lie (super)algebras to physics, etc. 1942

17B99

None of the above, but in this section 1097

17Cxx

Jordan algebras (algebras, triples and pairs) 2642

17C05

Identities and free Jordan structures 205

17C10

Structure theory for Jordan algebras 598

17C17

Radicals in Jordan algebras 39

17C20

Simple, semisimple Jordan algebras 278

17C27

Idempotents, Peirce decompositions 87

17C30

Associated groups, automorphisms of Jordan algebras 136

17C36

Associated manifolds of Jordan algebras 47

17C37

Associated geometries of Jordan algebras 47

17C40

Exceptional Jordan structures 155

17C50

Jordan structures associated with other structures [See also 16W10] 522

17C55

Finite-dimensional structures of Jordan algebras 111

17C60

Division algebras and Jordan algebras 46

17C65

Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 652

17C70

Super structures 175

17C90

Applications of Jordan algebras to physics, etc. 37

17C99

None of the above, but in this section 204

17Dxx

Other nonassociative rings and algebras 2451

17D05

Alternative rings 887

17D10

Mal’tsev rings and algebras 281

17D15

Right alternative rings 144

17D20

\((\gamma, \delta)\)-rings, including \((1,-1)\)-rings 96

17D25

Lie-admissible algebras 275

17D30

(non-Lie) Hom algebras and topics 2

17D92

Genetic algebras 432

17D99

None of the above, but in this section 566

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Mathematics Subject Classification – MSC2020

Overview