17XX 


Nonassociative rings and algebras 


1700 
General reference works (handbooks, dictionaries, bibliographies, etc.) 


1701 
Instructional exposition (textbooks, tutorial papers, etc.) 


1702 
Research exposition (monographs, survey articles) 


1703 
Historical (must also be assigned at least one classification number from Section 01) 


1704 
Explicit machine computation and programs (not the theory of computation or programming) 


1706 
Proceedings, conferences, collections, etc. 


1708 
Computational methods 


17A01 
General theory 


17A05 
Powerassociative rings 


17A15 
Noncommutative Jordan algebras 


17A20 
Flexible algebras 


17A30 
Algebras satisfying other identities 


17A32 
Leibniz algebras 


17A35 
Division algebras 


17A36 
Automorphisms, derivations, other operators 


17A40 
Ternary compositions 


17A42 
Other $n$ary compositions $(n \ge 3)$ 


17A45 
Quadratic algebras (but not quadratic Jordan algebras) 


17A50 
Free algebras 


17A60 
Structure theory 


17A65 
Radical theory 


17A70 
Superalgebras 


17A75 
Composition algebras 


17A80 
Valued algebras 


17A99 
None of the above, but in this section 


17B01 
Identities, free Lie (super)algebras 


17B05 
Structure theory 


17B08 
Coadjoint orbits; nilpotent varieties 


17B10 
Representations, algebraic theory (weights) 


17B15 
Representations, analytic theory 


17B20 
Simple, semisimple, reductive (super)algebras 


17B22 
Root systems 


17B25 
Exceptional (super)algebras 


17B30 
Solvable, nilpotent (super)algebras 


17B35 
Universal enveloping (super)algebras [See also 16S30] 


17B37 
Quantum groups (quantized enveloping algebras) and related deformations [See also 16T20, 20G42, 81R50, 82B23] 


17B40 
Automorphisms, derivations, other operators 


17B45 
Lie algebras of linear algebraic groups [See also 14Lxx and 20Gxx] 


17B50 
Modular Lie (super)algebras 


17B55 
Homological methods in Lie (super)algebras 


17B56 
Cohomology of Lie (super)algebras 


17B60 
Lie (super)algebras associated with other structures (associative, Jordan, etc.) [See also 16W10, 17C40, 17C50] 


17B62 
Lie bialgebras; Lie coalgebras 


17B63 
Poisson algebras 


17B65 
Infinitedimensional Lie (super)algebras [See also 22E65] 


17B66 
Lie algebras of vector fields and related (super) algebras 


17B67 
KacMoody (super)algebras; extended affine Lie algebras; toroidal Lie algebras 


17B68 
Virasoro and related algebras 


17B69 
Vertex operators; vertex operator algebras and related structures 


17B70 
Graded Lie (super)algebras 


17B75 
Color Lie (super)algebras 


17B80 
Applications to integrable systems 


17B81 
Applications to physics 


17B99 
None of the above, but in this section 


17C05 
Identities and free Jordan structures 


17C10 
Structure theory 


17C17 
Radicals 


17C20 
Simple, semisimple algebras 


17C27 
Idempotents, Peirce decompositions 


17C30 
Associated groups, automorphisms 


17C36 
Associated manifolds 


17C37 
Associated geometries 


17C40 
Exceptional Jordan structures 


17C50 
Jordan structures associated with other structures [See also 16W10] 


17C55 
Finitedimensional structures 


17C60 
Division algebras 


17C65 
Jordan structures on Banach spaces and algebras [See also 46H70, 46L70] 


17C70 
Super structures 


17C90 
Applications to physics 


17C99 
None of the above, but in this section 


17D05 
Alternative rings 


17D10 
Malʹcev (Malʹtsev) rings and algebras 


17D15 
Right alternative rings 


17D20 
$(\gamma, \delta)$rings, including $(1,1)$rings 


17D25 
Lieadmissible algebras 


17D92 
Genetic algebras 


17D99 
None of the above, but in this section 