Hokkaido Mathematical Journal, ISSN 0385-4035, 2011, Volume 40, Issue 3, pp. 375 - 392

Let A be an irreducible Coxeter arrangement and k be a multiplicity of A. We study the derivation module D(A, k...

Multi-arrangement | Primitive derivation | Coxeter arrangement | Logarithmic differential form | Coxeter group | Multi-derivation module | logarithmic differential form | multi-arrangement | MATHEMATICAL & COMPUTATIONAL BIOLOGY | multi-derivation module | primitive derivation

Multi-arrangement | Primitive derivation | Coxeter arrangement | Logarithmic differential form | Coxeter group | Multi-derivation module | logarithmic differential form | multi-arrangement | MATHEMATICAL & COMPUTATIONAL BIOLOGY | multi-derivation module | primitive derivation

Journal Article

Communications in Algebra, ISSN 0092-7872, 11/2010, Volume 38, Issue 11, pp. 4348 - 4361

Let Q ∈ [x 1 ,..., x n ] = S be a homogeneous polynomial of degree d. The freeness of the logarithmic derivation module, D(Q...

Logarithmic derivation module | Graded Betti numbers | MATHEMATICS | ARRANGEMENT | FORMULA | Derivation | Algebra | Equivalence | Modules

Logarithmic derivation module | Graded Betti numbers | MATHEMATICS | ARRANGEMENT | FORMULA | Derivation | Algebra | Equivalence | Modules

Journal Article

Journal of the Mathematical Society of Japan, ISSN 0025-5645, 2018, Volume 70, Issue 3, pp. 975 - 988

.... We compute the Chern class of the sheaf of logarithmic derivations along D and compare it with the Chern-Schwartz-MacPherson class of the hypersurface complement...

Jacobian ideal of linear type | Logarithmic derivation | And Phrases. Chern–Schwartz–MacPherson class | MATHEMATICS | MODULE | logarithmic derivation | Chern-Schwartz-MacPherson class | SINGULAR ALGEBRAIC-VARIETIES

Jacobian ideal of linear type | Logarithmic derivation | And Phrases. Chern–Schwartz–MacPherson class | MATHEMATICS | MODULE | logarithmic derivation | Chern-Schwartz-MacPherson class | SINGULAR ALGEBRAIC-VARIETIES

Journal Article

Mathematical Research Letters, ISSN 1073-2780, 2017, Volume 24, Issue 1, pp. 153 - 172

...) ideals whose logarithmic derivation module is free, in (not necessarily regular) factorial domains essentially of finite type over a field of characteristic zero...

Derivation | Logarithmic derivation | Free divisor | Zariski-Lipman conjecture | free divisor | MATHEMATICS | logarithmic derivation | DISCRIMINANTS | CONJECTURE

Derivation | Logarithmic derivation | Free divisor | Zariski-Lipman conjecture | free divisor | MATHEMATICS | logarithmic derivation | DISCRIMINANTS | CONJECTURE

Journal Article

Journal of Algebra, ISSN 0021-8693, 2011, Volume 330, Issue 1, pp. 251 - 262

We define primitive derivations for Coxeter arrangements which may not be irreducible. Using those derivations, we introduce the primitive filtrations...

Logarithmic differential 1-forms | Coxeter groups | Hodge filtrations | Coxeter arrangements | Arrangements of hyperplanes | Basic invariants | Primitive derivations | MATHEMATICS | Mechanical engineering

Logarithmic differential 1-forms | Coxeter groups | Hodge filtrations | Coxeter arrangements | Arrangements of hyperplanes | Basic invariants | Primitive derivations | MATHEMATICS | Mechanical engineering

Journal Article

Canadian mathematical bulletin, ISSN 0008-4395, 03/2018, Volume 61, Issue 1, pp. 166 - 173

...) algebraic variety deûned over a field $k$ of characteristic zero, then $X$ is a hypersurface if and only if the module ${{T}_{{{O}_{{{\mathbb{A}}^{n\,/k}}}(X...

free divisor | MATHEMATICS | FREE DIVISORS | logarithmic derivation | FREE ARRANGEMENT | DISCRIMINANTS | FREENESS | P-2 | hypersurface | logarithmic vector field | HYPERPLANES

free divisor | MATHEMATICS | FREE DIVISORS | logarithmic derivation | FREE ARRANGEMENT | DISCRIMINANTS | FREENESS | P-2 | hypersurface | logarithmic vector field | HYPERPLANES

Journal Article

Communications in Algebra, ISSN 0092-7872, 07/2019, Volume 47, Issue 7, pp. 2654 - 2666

In this note, we study the logarithmic derivation module of a non-free arrangement...

Hyperplane arrangements | logarithmic derivations | MATHEMATICS | Derivation | Lower bounds | Addition theorem

Hyperplane arrangements | logarithmic derivations | MATHEMATICS | Derivation | Lower bounds | Addition theorem

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2013, Volume 63, Issue 3, pp. 1177 - 1203

Let Y be a divisor on a smooth algebraic variety X. We investigate the geometry of the Jacobian scheme of Y, homological invariants derived from logarithmic...

Logarithmic | Hyperplane arrangement | Free divisor | Differential form | free divisor | differential form | COMPLEMENT | ARRANGEMENT | logarithmic | POWERS | LINEAR FREE DIVISORS | DERIVATIONS | MATHEMATICS | hyperplane arrangement | MODULE | CURVE | FREE RESOLUTION | HYPERPLANES

Logarithmic | Hyperplane arrangement | Free divisor | Differential form | free divisor | differential form | COMPLEMENT | ARRANGEMENT | logarithmic | POWERS | LINEAR FREE DIVISORS | DERIVATIONS | MATHEMATICS | hyperplane arrangement | MODULE | CURVE | FREE RESOLUTION | HYPERPLANES

Journal Article

JOURNAL OF THE MATHEMATICAL SOCIETY OF JAPAN, ISSN 0025-5645, 10/2019, Volume 71, Issue 4, pp. 1027 - 1047

We introduce a new algebra associated with a hyperplane arrangement A, called the Solomon-Terao algebra ST(A, eta), where eta is a homogeneous polynomial. It...

MATHEMATICS | logarithmic derivation modules | EXPONENTS | complete intersection ring | free arrangements | Solomon-Terao formula | hyperplane arrangements | Artinian ring

MATHEMATICS | logarithmic derivation modules | EXPONENTS | complete intersection ring | free arrangements | Solomon-Terao formula | hyperplane arrangements | Artinian ring

Journal Article

Journal of Algebra, ISSN 0021-8693, 01/2018, Volume 493, pp. 20 - 35

...]. However, there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended Catalan and Shi arrangements...

Weyl group | Shi arrangement | Hyperplane arrangement | Catalan arrangement | Logarithmic derivation | Affine Weyl group | Free arrangement

Weyl group | Shi arrangement | Hyperplane arrangement | Catalan arrangement | Logarithmic derivation | Affine Weyl group | Free arrangement

Journal Article

01/2010, ISBN 9814273244

Book Chapter

Journal of algebraic combinatorics, ISSN 1572-9192, 2016, Volume 45, Issue 1, pp. 171 - 189

.... We apply this construction to the module of derivations of a graphic multi-arrangement, yielding homological criteria for bounding its projective dimension and determining freeness...

05E40 | Primary 13P20 | Hyperhomology | Mathematics | Multi-derivations | Secondary 13D02 | 32S22 | Multi-arrangements | Convex and Discrete Geometry | Graphic arrangements | Generalized splines | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Chordal graphs | Logarithmic derivations | MULTIPLICITY | CONJECTURE | TORIC VARIETIES | MATHEMATICS | EQUIVARIANT CHOW COHOMOLOGY | HYPERPLANES

05E40 | Primary 13P20 | Hyperhomology | Mathematics | Multi-derivations | Secondary 13D02 | 32S22 | Multi-arrangements | Convex and Discrete Geometry | Graphic arrangements | Generalized splines | Order, Lattices, Ordered Algebraic Structures | Group Theory and Generalizations | Combinatorics | Computer Science, general | Chordal graphs | Logarithmic derivations | MULTIPLICITY | CONJECTURE | TORIC VARIETIES | MATHEMATICS | EQUIVARIANT CHOW COHOMOLOGY | HYPERPLANES

Journal Article

INVENTIONES MATHEMATICAE, ISSN 0020-9910, 03/2017, Volume 207, Issue 3, pp. 1239 - 1287

.... We use this Liouville complex to connect properties of the D-module generated by to homological data of the Jacobian ideal...

MATHEMATICS | FREE DIVISORS | ZETA-FUNCTIONS | LOGARITHMIC COMPARISON THEOREM | B-FUNCTIONS | COMPLEXES | SINGULARITY | DUALITY | HYPERPLANE ARRANGEMENTS | DIFFERENTIAL-OPERATORS | IDEALS

MATHEMATICS | FREE DIVISORS | ZETA-FUNCTIONS | LOGARITHMIC COMPARISON THEOREM | B-FUNCTIONS | COMPLEXES | SINGULARITY | DUALITY | HYPERPLANE ARRANGEMENTS | DIFFERENTIAL-OPERATORS | IDEALS

Journal Article

Collectanea Mathematica, ISSN 0010-0757, 05/2016, Volume 67, Issue 2, pp. 311 - 328

... in commutative Noetherian rings containing the rational numbers. Our approach is through the study of general logarithmic derivation modules, here dubbed tangential...

Derivation | Differential ideal | Primary decomposition | Logarithmic derivation | CRITERIA | MATHEMATICS | MATHEMATICS, APPLIED | DERIVATIONS

Derivation | Differential ideal | Primary decomposition | Logarithmic derivation | CRITERIA | MATHEMATICS | MATHEMATICS, APPLIED | DERIVATIONS

Journal Article

Journal of Algebra, ISSN 0021-8693, 2009, Volume 322, Issue 8, pp. 2839 - 2847

We study structures of derivation modules of Coxeter multiarrangements with quasi-constant multiplicities by using the primitive derivation...

Hyperplane arrangements | Coxeter arrangements | Logarithmic vector fields | MATHEMATICS | FREE ARRANGEMENT | CONTACT-ORDER FILTRATION | DERIVATIONS

Hyperplane arrangements | Coxeter arrangements | Logarithmic vector fields | MATHEMATICS | FREE ARRANGEMENT | CONTACT-ORDER FILTRATION | DERIVATIONS

Journal Article

16.
Full Text
A basis construction of the extended Catalan and Shi arrangements of the type &ITA&IT2

JOURNAL OF ALGEBRA, ISSN 0021-8693, 01/2018, Volume 493, pp. 20 - 35

...]. However, there have been no explicit constructions of the bases for the logarithmic derivation modules of the extended Catalan and Shi arrangements...

Weyl group | MATHEMATICS | Shi arrangement | Hyperplane arrangement | Catalan arrangement | Logarithmic derivation | Affine Weyl group | Free arrangement | COXETER ARRANGEMENTS

Weyl group | MATHEMATICS | Shi arrangement | Hyperplane arrangement | Catalan arrangement | Logarithmic derivation | Affine Weyl group | Free arrangement | COXETER ARRANGEMENTS

Journal Article

17.
Full Text
A criterion for the logarithmic differential operators to be generated by vector fields

Proceedings of the American Mathematical Society, ISSN 0002-9939, 11/2007, Volume 135, Issue 11, pp. 3631 - 3640

... the divisors for which LCT holds Let be the -module of holomorphic vector fields on X and D be the -submodule of logarithmic differential operators along D Sai80 A divisor...

Algebra | Differential operators | Mathematical theorems | Vector fields | Hyperplanes | Differentials | Coordinate systems | Mathematics | Mathematical rings | Computer algebra systems | V-filtration | Symmetric algebra | Hyperplane arrangement | Free divisor | Logarithmic differential operator | free divisor | MATHEMATICS | MATHEMATICS, APPLIED | hyperplane arrangement | MODULE | logarithmic differential operator | symmetric algebra

Algebra | Differential operators | Mathematical theorems | Vector fields | Hyperplanes | Differentials | Coordinate systems | Mathematics | Mathematical rings | Computer algebra systems | V-filtration | Symmetric algebra | Hyperplane arrangement | Free divisor | Logarithmic differential operator | free divisor | MATHEMATICS | MATHEMATICS, APPLIED | hyperplane arrangement | MODULE | logarithmic differential operator | symmetric algebra

Journal Article

18.
Full Text
Fusion in the entwined category of Yetter-Drinfeld modules of a rank-1 Nichols algebra

Theoretical and mathematical physics, ISSN 1573-9333, 2012, Volume 173, Issue 1, pp. 1329 - 1358

.... Together with the decomposition that we find for the product of simple Yetter-Drinfeld modules, this strongly suggests that the relevant Nichols algebra furnishes an equivalence with the triplet W-algebra in the (p, 1...

fusion | Theoretical, Mathematical and Computational Physics | Yetter-Drinfeld module | Nichols algebra | Applications of Mathematics | logarithmic conformal field theory | Physics | EXTENSIONS | PHYSICS, MULTIDISCIPLINARY | POINTED HOPF-ALGEBRAS | QUANTUM GROUPS | INVARIANTS | MINIMAL MODELS | CLASSIFICATION | PHYSICS, MATHEMATICAL | CONFORMAL FIELD-THEORY | W-ALGEBRA | GROUP-REPRESENTATIONS | CROSSED-MODULES

fusion | Theoretical, Mathematical and Computational Physics | Yetter-Drinfeld module | Nichols algebra | Applications of Mathematics | logarithmic conformal field theory | Physics | EXTENSIONS | PHYSICS, MULTIDISCIPLINARY | POINTED HOPF-ALGEBRAS | QUANTUM GROUPS | INVARIANTS | MINIMAL MODELS | CLASSIFICATION | PHYSICS, MATHEMATICAL | CONFORMAL FIELD-THEORY | W-ALGEBRA | GROUP-REPRESENTATIONS | CROSSED-MODULES

Journal Article

Journal of High Energy Physics, ISSN 1126-6708, 09/2007, Volume 2007, Issue 9, pp. 085 - 85

Extending our earlier work on PSL(2|2), we explain how to reduce the solution of WZNW models on general type I supergroups to those defined on the bosonic...

Conformal and W symmetry | Superspaces | Conformal field models in string theory | Space-time symmetries | conformal and W symmetry | conformal field models in string theory | WEIGHT MODULES | WZW-MODEL | superspaces | space-time symmetries | ZUMINO-WITTEN MODEL | ALGEBRAS | REPRESENTATION-THEORY | SIGMA-MODELS | CONSTRUCTION | SUPERALGEBRAS | CONFORMAL FIELD-THEORIES | LOGARITHMIC OPERATORS | PHYSICS, PARTICLES & FIELDS

Conformal and W symmetry | Superspaces | Conformal field models in string theory | Space-time symmetries | conformal and W symmetry | conformal field models in string theory | WEIGHT MODULES | WZW-MODEL | superspaces | space-time symmetries | ZUMINO-WITTEN MODEL | ALGEBRAS | REPRESENTATION-THEORY | SIGMA-MODELS | CONSTRUCTION | SUPERALGEBRAS | CONFORMAL FIELD-THEORIES | LOGARITHMIC OPERATORS | PHYSICS, PARTICLES & FIELDS

Journal Article

10/2018, ISBN 1107187737

This graduate textbook offers a self-contained introduction to the concepts and techniques of logarithmic geometry, a key tool for analyzing compactification...

eBook

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