A retrospect of the research in nonassociative algebras in IME-USP
From MaRDI portal
Publication:2082030
DOI10.1007/s40863-021-00248-xzbMath1502.17001OpenAlexW3185528010WikidataQ121627484 ScholiaQ121627484MaRDI QIDQ2082030
Luiz Antonio Peresi, Ivan Pavlovic Shestakov, Lucia S. I. Murakami
Publication date: 30 September 2022
Published in: São Paulo Journal of Mathematical Sciences (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s40863-021-00248-x
Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02) History of nonassociative rings and algebras (17-03)
Cites Work
- Irreductible representations of the simple Jordan superalgebra of Grassmann Poisson bracket
- Simple finite-dimensional noncommutative Jordan superalgebras of characteristic 0
- Deformations of Jordan algebras of dimension four
- Nilpotent Sabinin algebras
- Polynomial and Poisson dependence in free Poisson algebras and free Poisson fields
- Filtered multiplicative bases of restricted enveloping algebras
- On simple Lie algebras of dimension seven over fields of characteristic \(2\)
- Normal enveloping algebras
- Prime \((-1,1)\) and Jordan monsters and superalgebras of vector type
- Basic superranks for varieties of algebras
- Cyclic extensions of finite simple groups
- On the Tits-Kantor-Koecher construction of unital Jordan bimodules
- Nil graded self-similar algebras
- Jordan gradings on associative algebras.
- Associative identities of octonions
- Finite-dimensional non-associative algebras and codimension growth
- Nilpotency in Bernstein algebras
- Noncommutative Jordan superalgebras of degree \(n \geq 2\)
- Representation type of Jordan algebras
- Commutative Moufang loops and alternative algebras.
- Constants of partial derivations and primitive operations
- Superalgebras and counterexamples
- Invariants of \(\mathrm G_2\) and Spin(7) in positive characteristic
- Nonhomogeneous subalgebras of Lie and special Jordan superalgebras
- Speciality of Malcev superalgebras on one odd generator
- Examples of self-iterating Lie algebras
- Co-Moufang deformations of the universal enveloping algebra of the algebra of traceless octonions
- An application of lattice basis reduction to polynomial identities for algebraic structures
- Skew-symmetric identities of octonions
- Sylow's theorem for Moufang loops.
- A base of the free alternative superalgebra on one odd generator
- On baric algebras with prescribed automorphisms
- Semi-prime Bernstein algebras
- A note on duplication of algebras
- On derivations of baric algebras with prescribed automorphisms
- Finite basis property of identities of associative algebras
- A criterion for finitely generated Bernstein algebras to be genetic
- Local algebras of a multidimensional three-web
- A class of nonassociative algebras with involution containing the class of Jordan algebras
- Polynomial identities of Bernstein algebras of small dimension
- Graphs and nonassociative algebras
- Every Akivis algebra is linear
- Indecomposable baric algebras. II
- Shape identities in genetic algebras
- Identities of Cayley-Dickson algebras
- On identities of baric algebras and superalgebras
- Some properties of the automorphisms of a Bernstein algebra
- An envelope for Malcev algebras.
- The radical in alternative baric algebras
- Free Akivis algebras, primitive elements, and hyperalgebras
- Wedderburn principal theorem for Jordan superalgebras. I
- Commuting \(U\)-operators and nondegenerate imbeddings of Jordan systems
- Automorphism groups of diagonal \(\mathbb{Z}_p\)-forms of the Lie algebra \(sl_2(\mathbb{Q}_p)\), \(p > 2\)
- Simple finite-dimensional modular noncommutative Jordan superalgebras
- Gradings on simple Jordan and Lie algebras
- The bar-radical of baric algebras
- Noncommutative Jordan superalgebras of degree \(n > 2\)
- Solutions of the Bernstein problem in the nonregular case
- Loop of formal diffeomorphisms and Faà di Bruno coloop bialgebra
- On the free Jordan algebras
- Right alternative bimodules over Cayley algebra and coordinatization theorem
- The Freiheitssatz for generic Poisson algebras
- The coordinate ring of an \(n\)-dimensional sphere and some examples of differentially simple algebras
- On filtered multiplicative bases of some associative algebras.
- Indecomposable baric algebras
- A characterization of Lie algebras of skew-symmetric elements
- Geometric classification of nilpotent Jordan algebras of dimension five
- Finite-dimensional right alternative superalgebras with semisimple strongly alternative even part
- Kronecker factorization theorems for alternative superalgebras
- Some examples of nil Lie algebras
- Special identities for Bol algebras
- Branch rings, thinned rings, tree enveloping rings.
- Nilpotence of a class of commutative power-associative nilalgebras
- Commutative power-associative nilalgebras of nilindex 5
- TWO NUMERICAL INVARIANTS FOR BERNSTEIN ALGEBRAS
- CONSTRUCTION OF NON-FINITELY BASED T-IDEALS
- GRADINGS OF SIMPLE JORDAN ALGEBRAS AND THEIR RELATION TO THE GRADINGS OF SIMPLE ASSOCIATIVE ALGEBRAS
- Representations of exceptional simple alternative superalgebras of characteristic 3
- Irreducible bimodules over alternative algebras and superalgebras
- On Right Alternative Superalgebras
- The variety of three-dimensional real Jordan algebras
- Abelian-by-Cyclic Moufang Loops
- DESCRIPTION OF SIMPLE MODULES FOR SCHUR SUPERALGEBRA S(2|2)
- On the radical of a free Malcev algebra
- Automorphic equivalence of the representations of Lie algebras
- On Power-Associative Nilalgebras of Dimension N and Nilindex N-1
- On Free Sabinin Algebras
- Automorphic loops arising from module endomorphisms
- ON SPECIALITY OF BINARY-LIE ALGEBRAS
- Algebraic Bol loops
- Polynomial Identities of Finite Dimensional Simple Algebras
- Structurable Superalgebras of Classical Type
- Description of costandard modules for Schur superalgebraS(2|1) in positive characteristic
- Special Identities for Quasi-Jordan Algebras
- Commutative Power-Associative Algebras of Nilindex Four
- On associative representations of non-associative algebras
- Malcev dialgebras
- JORDAN SUPERALGEBRAS DEFINED BY BRACKETS
- On Commutative Power-Associative Nilalgebras
- Solvability of commutative automorphic loops
- Commuting $U$-operators in Jordan algebras
- Polynomial identities for the ternary cyclic sum
- Kimmerle conjecture for the Held and O'Nan sporadic simple groups
- The Bar-Radical of a Class of Almost Alternative Baric Algebras
- The Chevalley and Costant theorems for Mal’tsev algebras
- Noetherianness of wreath products of Abelian Lie algebras with respect to equations of universal enveloping algebra
- Nuclear Elements of Degree 6 in the Free Alternative Algebra
- Jordan bimodules over the superalgebras 𝑃(𝑛) and 𝑄(𝑛)
- An infinite dimensional affine nil algebra with finite Gelfand-Kirillov dimension
- On a construction of self-dual gauge fields in seven dimensions
- Polynomial Identities for Bernstein Algebras of Simple Mendelian Inheritance
- On the derivations of gametic algebras for polyploidy with multiple alleles
- On the derivation algebra of zygotic algebras for polyploidy with multiple alleles
- Genetic Algebras Satisfying Bernstein's Stationarity Principle
- A radical splitting theorem for bernstein algebras
- On the multiplication algebra of a bernstein algebra*
- Invariance of dimension ofp-subspaces in bernstein algebras*
- Solvability of the ideal of all weight zero elements in bernstein algebras
- On the Structure of Bernstein Algebras
- Low Dimensional Bernstein-Jordan Algebras
- Algebraic structure of genetic inheritance
- A class of exceptional bernstein algebras associated to graphs1
- On nilpotency of the barideal of a bernstein algebra
- Moufang loops and alternative algebras
- Poisson brackets and two-generated subalgebras of rings of polynomials
- The tame and the wild automorphisms of polynomial rings in three variables
- FREE MALCEV SUPERALGEBRA ON ONE ODD GENERATOR
- On idempotents and isomorphisms of multiplication algebras of bernstein algebras
- Counterexamples to the Specht problem
- Free generic Poisson fields and algebras
- A non-associative Baker-Campbell-Hausdorff formula
- Derivations of the Lie algebra of infinite strictly upper triangular matrices over a commutative ring
- Description of costandard modules for Schur superalgebra S(2|2) in positive characteristic
- A finite presentation of Jordan algebras
- Rings of constants of linear derivations on Fermat rings
- Nilpotent Steiner loops of class 2
- COMMUTATIVE AUTOMORPHIC LOOPS OF ORDER p3
- REPRESENTATIONS OF EXCEPTIONAL SIMPLE JORDAN SUPERALGEBRAS OF CHARACTERISTIC 3#
- Some graded identities of the Cayley–Dickson algebra
- A Nonzero Element of Degree 7 in the Center of the Free Alternative Algebra
- The multiplication algebra of a bernstein algebra: basic results
- Central Quotients and Coverings of Steinberg Unitary Lie Algebras
- The free commutative automorphic $2$-generated loop of nilpotency class $3$
- Higher identities for the ternary commutator
- Locally nilpotent derivations and automorphisms of free associative algebra with two generators
- Hopf algebras in non-associative Lie theory
- The Wedderburn b-decomposition for a class of almost alternative baric algebras
- The Nucleus of the Free Alternative Algebra
- Lagrange's theorem for Moufang loops
- THE FREE ALTERNATIVE SUPERALGEBRA ON ONE ODD GENERATOR
- PBW-Pairs of Varieties of Linear Algebras
- Simple Classical Lie Algebras in Characteristic 2 and Their Gradations, II
- ASSOCIATIVE NIL-ALGEBRAS OVER FINITE FIELDS
- Classification of Trilinear Operations
- The Nagata automorphism is wild
- The Universal Multiplicative Envelope of the Free Malcev Superalgebra on One Odd Generator
- GROUPS WITH TRIALITY
- Free Steiner triple systems and their automorphism groups
- Special train algebras arising in genetics II
- On Commuting U-Operators in Jordan Algebras
- Multiplication formulas in Moufang loops
- Jordan Superalgebras of Type and the Wedderburn Principal Theorem (WPT)
- Structurable superalgebras of Cartan type
- Structurable superalgebras of Cartan type
- Speciality of Lie-Jordan algebras
- Irreducible unital right alternative bimodules
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
This page was built for publication: A retrospect of the research in nonassociative algebras in IME-USP