Advances in Mathematics, ISSN 0001-8708, 04/2019, Volume 346, pp. 510 - 545

We introduce the notion of a holonomic D-module on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In...

Duality | D-modules | Perverse t-structure | Logarithmic geometry | MATHEMATICS | INFINITE ROOT STACKS | DUALIZING COMPLEXES | PARABOLIC SHEAVES | Mathematics - Algebraic Geometry

Duality | D-modules | Perverse t-structure | Logarithmic geometry | MATHEMATICS | INFINITE ROOT STACKS | DUALIZING COMPLEXES | PARABOLIC SHEAVES | Mathematics - Algebraic Geometry

Journal Article

Journal of Physics A: Mathematical and Theoretical, ISSN 1751-8113, 07/2017, Volume 50, Issue 34, pp. 1 - 24

We utilise bosonic Fock spaces, considered as Virasoro modules, to make free field realisations of the so-called staggered modules of two-dimensional...

indecomposable representation | β-invariant | free field | logarithmic CFT | staggered modules | free boson | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | MINIMAL MODELS | PARAMETERS | PHYSICS, MATHEMATICAL | VIRASORO | ALGEBRAS | CONFORMAL FIELD-THEORY | INTERTWINING-OPERATORS | FUSION PRODUCTS | beta-invariant

indecomposable representation | β-invariant | free field | logarithmic CFT | staggered modules | free boson | REPRESENTATIONS | PHYSICS, MULTIDISCIPLINARY | MINIMAL MODELS | PARAMETERS | PHYSICS, MATHEMATICAL | VIRASORO | ALGEBRAS | CONFORMAL FIELD-THEORY | INTERTWINING-OPERATORS | FUSION PRODUCTS | beta-invariant

Journal Article

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, ISSN 1751-8113, 01/2010, Volume 43, Issue 4

Based on symmetry principles, we derive a fusion algebra generated from repeated fusions of the irreducible modules appearing in the W-extended logarithmic...

LOGARITHMIC MINIMAL MODELS | PHYSICS, MULTIDISCIPLINARY | BOUNDARY-CONDITIONS | FIELD-THEORY | PRODUCTS | RINGS | POTENTIALS | PHYSICS, MATHEMATICAL | Physics - High Energy Physics - Theory

LOGARITHMIC MINIMAL MODELS | PHYSICS, MULTIDISCIPLINARY | BOUNDARY-CONDITIONS | FIELD-THEORY | PRODUCTS | RINGS | POTENTIALS | PHYSICS, MATHEMATICAL | Physics - High Energy Physics - Theory

Journal Article

Theoretical and Mathematical Physics, ISSN 0040-5779, 10/2012, Volume 173, Issue 1, pp. 1329 - 1358

In the braided context, we rederive a popular nonsemisimple fusion algebra from a Nichols algebra. Together with the decomposition that we find for the product...

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

Compositio Mathematica, ISSN 0010-437X, 11/2010, Volume 146, Issue 6, pp. 1552 - 1616

Let K be a complete discrete valuation field of mixed characteristic (0, p) with a perfect residue field k. For a semi-stable scheme over the ring of integers...

nearby cycles | logarithmic scheme | module | MATHEMATICS | COMPLEX | CRYSTALLINE COHOMOLOGY | D-module | Integers | Residues | Construction | Spectra | Filtration | Crystal structure

nearby cycles | logarithmic scheme | module | MATHEMATICS | COMPLEX | CRYSTALLINE COHOMOLOGY | D-module | Integers | Residues | Construction | Spectra | Filtration | Crystal structure

Journal Article

NUCLEAR PHYSICS B, ISSN 0550-3213, 01/2020, Volume 950

This work concerns the representation theory of the affine Lie algebra A(1)((1)) at fractional level and its links to the representation theory of the Virasoro...

FOCK REPRESENTATIONS | FUSION RULES | VERMA MODULES | MINIMAL MODELS | LOGARITHMIC LIMITS | HIGHEST WEIGHT | DIMENSIONAL LIE-ALGEBRAS | JORDAN CELLS | NEVEU-SCHWARZ | COSET MODELS | PHYSICS, PARTICLES & FIELDS

FOCK REPRESENTATIONS | FUSION RULES | VERMA MODULES | MINIMAL MODELS | LOGARITHMIC LIMITS | HIGHEST WEIGHT | DIMENSIONAL LIE-ALGEBRAS | JORDAN CELLS | NEVEU-SCHWARZ | COSET MODELS | PHYSICS, PARTICLES & FIELDS

Journal Article

Journal of Algebra, ISSN 0021-8693, 2007, Volume 316, Issue 2, pp. 662 - 679

We describe an algorithm deciding if the annihilating ideal of the meromorphic function 1 f , where f = 0 defines an arrangement of hyperplanes, is generated...

Gröbner bases | Characteristic cycle | Hyperplane arrangements | Logarithmic [formula omitted]-modules | Localization | Logarithmic D-modules | localization | RHAM COMPLEXES | MATHEMATICS | LOCAL COHOMOLOGY GROUPS | FREE DIVISORS | grobner bases | LOGARITHMIC FORMS | hyperplane arrangements | logarithmic D-modules | ALGORITHMS | characteristic cycle | Algorithms

Gröbner bases | Characteristic cycle | Hyperplane arrangements | Logarithmic [formula omitted]-modules | Localization | Logarithmic D-modules | localization | RHAM COMPLEXES | MATHEMATICS | LOCAL COHOMOLOGY GROUPS | FREE DIVISORS | grobner bases | LOGARITHMIC FORMS | hyperplane arrangements | logarithmic D-modules | ALGORITHMS | characteristic cycle | Algorithms

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 03/2019, Volume 21, Issue 2, p. 1850008

This paper is a continuation of [D. Adamović and G. Radobolja, Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its...

self-dual modules | singular vectors | logarithmic representations | Whittaker modules | Heisenberg–Virasoro algebra | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | Heisenberg-Virasoro algebra | Algebra

self-dual modules | singular vectors | logarithmic representations | Whittaker modules | Heisenberg–Virasoro algebra | MATHEMATICS | MATHEMATICS, APPLIED | MODULES | Heisenberg-Virasoro algebra | Algebra

Journal Article

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). Any two-dimensional irreducible Coxeter...

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

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 of the...

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

IEEE Transactions on Microwave Theory and Techniques, ISSN 0018-9480, 11/2003, Volume 51, Issue 11, pp. 2203 - 2210

This paper presents a novel power-amplifier module (PAM) designed for GSM850-, GSM900 MHz, DCS1800- and PCS1900-MHz handset applications. The module combines...

Radio frequency | Power control | Dual band | Couplers | Detectors | Telephone sets | Radiofrequency integrated circuits | Manufacturing | Heterojunction bipolar transistors | Power generation | Directional coupler | Logarithmic amplifier (log-amp) | Power amplifier (PA) | logarithmic amplifier (logamp) | directional coupler | power amplifier (PA) | ENGINEERING, ELECTRICAL & ELECTRONIC | Amplifiers (Electronics) | Research | Mass production | Radio frequencies | Modules | Passive components | Calibration

Radio frequency | Power control | Dual band | Couplers | Detectors | Telephone sets | Radiofrequency integrated circuits | Manufacturing | Heterojunction bipolar transistors | Power generation | Directional coupler | Logarithmic amplifier (log-amp) | Power amplifier (PA) | logarithmic amplifier (logamp) | directional coupler | power amplifier (PA) | ENGINEERING, ELECTRICAL & ELECTRONIC | Amplifiers (Electronics) | Research | Mass production | Radio frequencies | Modules | Passive components | Calibration

Journal Article

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

For a germ f on a complex manifold X, we introduce a complex derived from the Liouville form acting on logarithmic differential forms, and give an exactness...

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

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), and of its natural...

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

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

We introduce and characterize the class of tangentially free ideals, which are (not necessarily principal) ideals whose logarithmic derivation module is free,...

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

International Journal of Mathematics, ISSN 0129-167X, 09/2006, Volume 17, Issue 8, pp. 975 - 1012

We describe a logarithmic tensor product theory for certain module categories for a "conformal vertex algebra". In this theory, which is a natural, although...

Logarithmic intertwining operators | Vertex tensor category | Braided tensor category | Generalized module | Conformal vertex algebra | MATHEMATICS | generalized module | logarithmic intertwining operators | conformal vertex algebra | CONFORMAL FIELD-THEORY | braided tensor category | vertex tensor category | CATEGORIES | Algebra

Logarithmic intertwining operators | Vertex tensor category | Braided tensor category | Generalized module | Conformal vertex algebra | MATHEMATICS | generalized module | logarithmic intertwining operators | conformal vertex algebra | CONFORMAL FIELD-THEORY | braided tensor category | vertex tensor category | CATEGORIES | Algebra

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 05/2017, Volume 369, Issue 5, pp. 3047 - 3066

In this paper, we solve Problem (A), present a solution of Problem (B) by Evertse and Gy]]>őő

Unit equations over finitely generated domains | Uniform bounds | Effective methods | MATHEMATICS | GROUP VARIETIES | effective methods | DECOMPOSABLE FORM EQUATIONS | LOGARITHMIC FORMS | UNIT EQUATIONS | uniform bounds

Unit equations over finitely generated domains | Uniform bounds | Effective methods | MATHEMATICS | GROUP VARIETIES | effective methods | DECOMPOSABLE FORM EQUATIONS | LOGARITHMIC FORMS | UNIT EQUATIONS | uniform bounds

Journal Article

Journal of Algebra, ISSN 0021-8693, 08/2017, Volume 484, pp. 88 - 108

In this paper, we prove that the categories of lower bounded twisted modules of positive integer levels for simple vertex operator algebras associated with...

Affine Lie algebras | Vertex operator algebras | Twisted Zhu's algebras | Logarithmic twisted modules | MATHEMATICS | Algebra

Affine Lie algebras | Vertex operator algebras | Twisted Zhu's algebras | Logarithmic twisted modules | MATHEMATICS | Algebra

Journal Article

International Journal of Mathematics, ISSN 0129-167X, 05/2016, Volume 27, Issue 5, p. 1650046

We construct a family of vertex algebras associated to the affine Lie algebra of polynomial current algebras of finite-dimensional abelian Lie algebras, along...

strongly graded vertex algebras | logarithmic modules | logarithmic tensor categories | Polynomial current algebras | MATHEMATICS | INTERTWINING-OPERATORS | Algebra

strongly graded vertex algebras | logarithmic modules | logarithmic tensor categories | Polynomial current algebras | MATHEMATICS | INTERTWINING-OPERATORS | Algebra

Journal Article

Annales de l'Institut Fourier, ISSN 0373-0956, 2018, Volume 68, Issue 2, pp. 725 - 766

We consider the germ of a reduced curve, possibly reducible. F. Delgado de la Mata proved that such a curve is Gorenstein if and only if its semigroup of...

Gorenstein curves | Values | Duality | Logarithmic residues | Equisingular deformations | SEMIGROUP | MATHEMATICS | logarithmic residues | MODULES | ANALYTIC CLASSIFICATION | HYPERSURFACES | values | equisingular deformations | SINGULARITY | DIFFERENTIALS | duality

Gorenstein curves | Values | Duality | Logarithmic residues | Equisingular deformations | SEMIGROUP | MATHEMATICS | logarithmic residues | MODULES | ANALYTIC CLASSIFICATION | HYPERSURFACES | values | equisingular deformations | SINGULARITY | DIFFERENTIALS | duality

Journal Article

Communications in Contemporary Mathematics, ISSN 0219-1997, 08/2012, Volume 14, Issue 4, pp. 1250029 - 1250066

Two related constructions are associated with screening operators in models of two-dimensional conformal field theory. One is a local system constructed in...

braiding | Nichols algebra | shuffle product | Logarithmic conformal field theory | screening operators | YetterDrinfeld modules | MATHEMATICS, APPLIED | POINTED HOPF-ALGEBRAS | QUANTUM GROUPS | TFT CONSTRUCTION | MINIMAL MODELS | DIAGONAL TYPE | MATHEMATICS | Yetter-Drinfeld modules | CONFORMAL FIELD-THEORY | W-ALGEBRAS | BRAIDED GROUPS | ROOT SYSTEMS | CROSSED-MODULES | Analysis | Algebra | Screening | Construction | Operators | Categories | Braiding | Mathematical models | Representations

braiding | Nichols algebra | shuffle product | Logarithmic conformal field theory | screening operators | YetterDrinfeld modules | MATHEMATICS, APPLIED | POINTED HOPF-ALGEBRAS | QUANTUM GROUPS | TFT CONSTRUCTION | MINIMAL MODELS | DIAGONAL TYPE | MATHEMATICS | Yetter-Drinfeld modules | CONFORMAL FIELD-THEORY | W-ALGEBRAS | BRAIDED GROUPS | ROOT SYSTEMS | CROSSED-MODULES | Analysis | Algebra | Screening | Construction | Operators | Categories | Braiding | Mathematical models | Representations

Journal Article

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