Georgia Benkart
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American mathematician
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Georgia Benkartmathematics Degrees
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Mathematics
Georgia Benkart's Degrees
- Bachelors Mathematics University of California, Berkeley
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Why Is Georgia Benkart Influential?
(Suggest an Edit or Addition)According to Wikipedia, Georgia McClure Benkart was an American mathematician who was known for her work in the structure and representation theory of Lie algebras and related algebraic structures. She published over 130 journal articles and co-authored three American Mathematical Society memoirs in four broad categories: modular Lie algebras; combinatorics of Lie algebra representations; graded algebras and superalgebras; and quantum groups and related structures.
Georgia Benkart's Published Works
Number of citations in a given year to any of this author's works
Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author
Published Works
- Lie algebras graded by finite root systems and intersection matrix algebras (1996) (150)
- G. Benkart, M. Chakrabarti, R. Leduc; C. Lee, J. Stroomer " Tensor product representations of general linear groups and their connections with Brauer algebras." (1994) (107)
- Two-Parameter Quantum Groups and Drinfel'd Doubles (2000) (97)
- Tableau Switching: Algorithms and Applications (1996) (80)
- On inner ideals and ad-nilpotent elements of Lie algebras (1977) (78)
- Lie algebras graded by the root system . (2003) (78)
- Crystal Bases for the Quantum Superalgebra $U_q(gl(m,n))$ (1998) (78)
- Crystal bases for the quantum superalgebra _ (2000) (74)
- Lie algebras graded by the root systems BCr, r ≧ 2 (2002) (67)
- Representations of Two-Parameter Quantum Groups and Schur-Weyl Duality (2001) (66)
- Modules with bounded weight multiplicities for simple Lie algebras (1997) (65)
- Central extensions of Lie algebras graded by finite root systems (2000) (65)
- Whittaker modules for generalized Weyl algebras (2008) (63)
- Down–Up Algebras (1998) (60)
- The centroid of extended affine and root graded Lie algebras (2005) (57)
- Tensor product representations for orthosymplectic Lie superalgebras (1996) (50)
- Quantized enveloping algebras for Borcherds superalgebras (1998) (50)
- The Derivation Algebra of a Real Division Algebra (1981) (50)
- Real Flexible Division Algebras (1982) (50)
- An investigation of real division algebras using derivations. (1981) (49)
- Graded Lie Algebras of Kac-Moody Type (1993) (47)
- A Hopf structure for down-up algebras (2001) (45)
- The Lie inner ideal structure of associative rings (1976) (41)
- The universal central extension of the three-point sl2 loop algebra (2005) (40)
- Derivations and automorphisms of nonassociative matrix algebras (1981) (37)
- Stability in modules for classical Lie algebras—a constructive approach (1990) (35)
- Motzkin algebras (2011) (34)
- New Irreducible Modules for Heisenberg and Affine Lie Algebras (2011) (34)
- Level 1 perfect crystals and path realizations of basic representations at q = 0 (2005) (33)
- Flexible Lie-admissible algebras (1981) (33)
- Finite-Dimensional Simple Lie Algebras with a Nonsingular Derivation (1995) (32)
- The Recognition Theorem for Graded Lie Algebras in Prime Characteristic (2005) (32)
- On the centre of two-parameter quantum groups (2006) (31)
- Lie superalgebras graded by the root system B(m,n) (2002) (30)
- Irreducible modules for the quantum affine algebra Uq(slˆ2) and its Borel subalgebra (2004) (29)
- Construction of Irreducible Representations over Khovanov-Lauda-Rouquier Algebras of Finite Classical Type (2011) (29)
- Lie algebras with self-centralizing ad-nilpotent elements (1979) (26)
- The equitable basis for $${\mathfrak{sl}_2}$$ (2008) (26)
- Lie algebras graded by the root systems ᵣ,≥2 (2002) (25)
- Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups (2016) (25)
- A new construction of the Kac Jordan superalgebra (2002) (24)
- Representations of rank one lie algebras of characteristic p (1982) (24)
- Rank one Lie algebras (1984) (23)
- Lie Algebras Graded by Root Systems (1994) (22)
- Derivations and Invariant Forms of Lie Algebras Graded by Finite Root Systems (1998) (22)
- Lie Superalgebras Graded by the Root Systems C(n), D(m, n), D(2, 1, α), F(4), G(3) (2002) (22)
- Partition Algebras and the Invariant Theory of the Symmetric Group (2017) (21)
- The Lie Inner Ideal Structure of Associative Rings Revisited (2009) (21)
- Chip firing on Dynkin diagrams and McKay quivers (2016) (20)
- Hopf algebras with triality (2011) (19)
- Indefinite Kac-Moody algebras of classical type (1994) (19)
- Power-associative Lie-admissible algebras (1984) (19)
- Partition algebras Pk(n) with 2k>n and the fundamental theorems of invariant theory for the symmetric group Sn (2017) (18)
- Graded Lie algebras with classical reductive null component (1989) (18)
- The Tits Construction and the Exceptional Simple Classical Lie Superalgebras (2003) (18)
- On the existence of ad-nilpotent elements (1977) (17)
- Albert-Zassenhaus Lie algebras and isomorphisms☆ (1979) (17)
- A Parametric Family of Subalgebras of the Weyl Algebra II. Irreducible Modules (2012) (16)
- Representations of algebraic groups, quantum groups, and Lie algebras : AMS-IMS-SIAM Joint Summer Research Conference, July 11-15, 2004, Snowbird Resort, Snowbird, Utah (2006) (16)
- Yetter-Drinfeld modules under cocycle twists (2009) (15)
- Some Constructions in the Theory of Locally Finite Simple Lie Algebras (2004) (15)
- A PARAMETRIC FAMILY OF SUBALGEBRAS OF THE WEYL ALGEBRA I. STRUCTURE AND AUTOMORPHISMS (2012) (15)
- The simple graded lie algebras of characteristic three with classical reductive component L 0 (1996) (14)
- Lie Algebras with Nilpotent Centralizers (1979) (14)
- Power-associative products on matrices (1982) (14)
- Indefinite Kac-Moody algebras of special linear type. (1995) (14)
- Quantum walled Brauer-Clifford superalgebras (2014) (13)
- Derivations of a parametric family of subalgebras of the Weyl algebra (2015) (13)
- Applications of isotopy to real division algebras (1981) (13)
- Tableaux and insertion schemes for spinor representations of the orthogonal Lie algebraso(2r + 1, C) (1991) (11)
- Tensor product Markov chains (2018) (10)
- Lie Algebras and Related Topics (1990) (10)
- Planar Rook Algebras and Tensor Representations of 𝔤𝔩(1 | 1) (2012) (9)
- Real division algebras and other algebras motivated by physics (1981) (9)
- Lie Algebras with Prescribed sl3 Decomposition (2011) (9)
- LIE G-TORI OF SYMPLECTIC TYPE (2005) (9)
- Derangements and tensor powers of adjoint modules for sl_n (2001) (9)
- Toral rank one Lie algebras (1988) (8)
- Isomorphism classes of Hamiltonian lie algebras (1989) (8)
- Poincar\'e Series for Tensor Invariants and the McKay Correspondence (2014) (8)
- Contributions to the classification of simple modular Lie algebras (1994) (8)
- A(n,n)-graded Lie superalgebras (2003) (8)
- A minimaj-preserving crystal on ordered multiset partitions (2017) (8)
- A quantum octonion algebra (1998) (8)
- Weight multiplicity polynomials for affine Kac-Moody algebras of type $A_r$ (1996) (7)
- The center of the affine nilTemperley–Lieb algebra (2015) (7)
- Derangements and Tensor Powers of Adjoint Modules for $$\mathfrak{s}\mathfrak{l}_n $$ (2002) (7)
- McKay centralizer algebras (2013) (6)
- Nilpotent Lie Algebras of Maximal Rank and of (2002) (6)
- Weighted Aztec Diamond Graphs and the Weyl Character Formula (2004) (6)
- Crystal Bases for Quantum Superalgebras (2000) (5)
- Simple modular lie algebras with 1-sections that are classical or solvable (1990) (5)
- A Parametric Family of Subalgebras of the Weyl Algebra III. Derivations (2014) (5)
- Unitary Lie Algebras and Lie Tori of Type BC_r, r \geq 3 (2008) (5)
- The Polynomial Behavior of Weight Multiplicities for the Affine Kac–Moody Algebras A(1)r (1998) (5)
- Weyl algebra modules (2002) (5)
- Construction of examples of Lie-admissible algebras (1982) (4)
- Multiparameter Weyl Algebras (2013) (4)
- Tensor power multiplicities for symmetric and alternating groups and dimensions of irreducible modules for partition algebras (2016) (3)
- Projection Maps for Tensor Products of gl(r, C)-Representations (1992) (3)
- Walks on graphs and their connections with tensor invariants and centralizer algebras (2016) (3)
- Some Problems in the Representation Theory of Simple Modular Lie Algebras (2015) (3)
- Simple Lie algebras of characteristic $p$ with dependent roots (1990) (3)
- Quantum group actions, twisting elements, and deformations of algebras (2005) (3)
- Cross products, invariants, and centralizers (2016) (3)
- Classical Lie Superalgebras Over Simple Associative Algebras (2006) (3)
- McKay matrices for finite-dimensional Hopf algebras (2020) (2)
- Irreducible Modules for the Quantum Affine Algebra $U_q(\hat{sl}_2)$ and its Borel subalgebra $U_q(\hat{sl}_2)^{\geq 0}$ (2003) (2)
- Q A ] 1 0 N ov 2 00 3 Irreducible Modules for the Quantum Affine Algebra U q ( ŝl 2 ) and its Borel Subalgebra U q ( ŝl 2 ) ≥ 0 (2)
- Lie Algebras, Madison 1987 (1989) (1)
- The Combinatorics of A 2-webs (2014) (1)
- Flexible Lie-admissible algebras with the solvable radical of A/sup -/ Abelian and Lie algebras with nondegenerate forms (1981) (1)
- A Schur-Weyl Duality Approach toWalking on Cubes (2014) (1)
- Derivations and automorphisms of matrices symmetric relative to a canonical involution (1980) (1)
- Representations of Rank 3 Algebras (2006) (1)
- Tensor Representations for the Drinfeld Double of the Taft Algebra (2020) (1)
- Abstract Algebra, By I. N. Herstein (1987) (1)
- Memories of Mary Ellen Rudin (2015) (1)
- The Polynomial Behavior of Weight Multiplicities for the Affine Kac-moody Algebras a Introduction (1998) (1)
- AWM at 50 and Beyond (2021) (1)
- Groups, Rings, Lie and Hopf Algebras III (2012) (0)
- R T ] 3 0 Se p 20 18 Tensor Product Markov Chains (0)
- The Combinatorics of $\mathsf{A_2}$-Webs (2013) (0)
- ( 1910 – 1999 ) (2000) (0)
- Lie algebras and related topics : proceedings of a research conference held May 22-June 1, 1988, with support from the National Science Foundation (1990) (0)
- Dimensions of irreducible modules for partition algebras and tensor power multiplicities for symmetric and alternating groups (2017) (0)
- A NEW CONSTRUCTION OF THE KAC (2002) (0)
- Chip firing on Dynkin diagrams and McKay quivers (2018) (0)
- The center of the affine nilTemperley–Lieb algebra (2016) (0)
- To Professor Robert Moody with our best wishes on his sixtieth birthday (0)
- TENSOR PRODUCT REPRESENTATIONS OF TEMPERLEY-LIEB ALGEBRAS AND THEIR CENTRALIZER ALGEBRAS (Topics in Young Diagrams and Representation Theory) (2002) (0)
- Lie Algebras, Madison 1987: Proceedings of a Workshop Held in Madison, Wisconsin, August 23-28, 1987 (1989) (0)
- Categories of Topological Isospaces and Isogroups ∗ (2014) (0)
- KAC-MOODY LIE ALGEBRAS GRADED BY KAC-MOODY ROOT SYSTEMS (2012) (0)
- A Schur-Weyl Duality Approach toWalking on Cubes (2016) (0)
- 2 1 Fe b 20 02 Weyl Algebra Modules (2008) (0)
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