Do not display this message again
Close window
LieAlgebras - DifferentialGeometry - Mathematics - Maple Help - Maplesoft
Products
Maple
• Maple Professional
• Maple Academic
• Maple Student Edition
• Maple Personal Edition
• Free Maple Player
• MapleNet
• Maple Toolboxes and Add-Ons
MapleSim
• MapleSim Professional
• MapleSim Academic
• MapleSim Server
• MapleSim Modelica Engine
• Connectors & Component Libraries
Online Education
• Maple T.A. - Testing & Assessment
• Maple T.A. MAA Placement Test Suite
• Möbius - Online Courseware
Other Products
• Toolboxes & Connectors
• E-Books & Study Guides
• Professional Services
• Partnerships and OEM Opportunities
Solutions
Education
• Mathematics Education
• Engineering Education
• High Schools & Two-Year Colleges
• Testing & Assessment
• Developmental Math
• Students
Applied Research
• Financial Modeling
• Operations Research
• High Performance Computing
• Physics
• Life Sciences
• Virtual Prototyping
Engineering: Industry Solutions
• Manufacturing
• Mining & Oil Production Equipment
• Aircraft Systems
• Space Systems
• Electric & Hybrid-Electric Vehicles
• Powertrain
• Vehicle Dynamics
• Heavy Vehicles (including trucks, off-road)
• Robotics Research
• Robotics/Motion Control/Mechatronics
• Power Industries
• Medical Devices
Engineering: Application Areas
• System Simulation & Analysis
• Model development for HIL
• Plant Modeling for Control Design
• Robotics/Motion Control/Mechatronics
• Vibration Analysis & Attenuation
• Battery Design
• Training Simulators
• Model-Predictive Control
• Product Design Validation & Optimization
• Analysis & Design Calculation Tools
• Machine Design
Purchase
• Purchase & Pricing
• Maplesoft Web Store
• Request a Price Quote
• Contact Maplesoft Sales
• Elite Maintenance Program
Support & Resources
Support
• Tech Support & Customer Service
• Frequently Asked Questions
• Online Product Help
• Product Documentation
• Download Product Updates
Product Training
• Online Product Training
• On-Site Training
Webinars & Events
• Live Webinars
• Recorded Webinars
• Upcoming Events
Content Hubs
• Teacher Resource Center
• Student Help Center
• Maplesoft Welcome Center
Publications
• Technical Whitepapers
• Application Briefs
• E-Mail Newsletters
• Maple Books
• Math Matters
Community
• MaplePrimes
• MapleCloud
Examples & Applications
• Maple Application Center
• MapleSim Model Gallery
• User Case Studies
• Exploring Engineering Fundamentals
• Teaching Concepts with Maple
Company
About Maplesoft
• Company Overview
• Management
• Customers
Media Center
• Media Releases
• User Case Studies
• Media Coverage
User Community
• MaplePrimes
• Maple Ambassador Program
Contact
• Global Contact Details
• Careers
Home
Products
Maple
MapleSim
The Möbius Project
Maple T.A.
Toolboxes and Connectors
Pricing & Purchase
Solutions
Education
Engineering
Applied Research
Support
Tech Support & Customer Service
FAQs
Online Product Help
Download Product Updates
Product Training
Resources
Live Webinars
Recorded Webinars
Teacher Resource Center
Student Help Center
Technical Whitepapers
E-mail Newsletters
Maple Application Center
MapleSim Model Gallery
User Case Studies
Exploring Engineering Fundamentals
Teaching Concepts with Maple
MaplePrimes
Company
About Maplesoft
Media Center
Contact
Careers
Toggle navigation
Online Help
All Products
Maple
MapleSim
Home
:
Support
:
Online Help
:
Mathematics
:
DifferentialGeometry
:
LieAlgebras
LieAlgebras
Sub Categories
LieAlgebraData
Query
Category Documents
Page 1 of 1
DifferentialGeometry/LieAlgebras/Adjoint
find the ad Matrix for a vector in a Lie algebra
DifferentialGeometry/LieAlgebras/AlgebraData
find the structure equations for a real algebra defined by a list of matrices and a multiplication procedure
DifferentialGeometry/LieAlgebras/AlgebraLibraryData
retrieve the structure equations for various classical algebras (quaternions, octonions, Clifford algebras, and low dimensional Jordan algebras)
DifferentialGeometry/LieAlgebras/AlgebraNorm
find the norm of a quaternion or octonion
DifferentialGeometry/LieAlgebras/ApplyHomomorphism
apply a Lie algebra homomorphism to a vector, form or tensor
DifferentialGeometry/LieAlgebras/AscendingIdealsBasis
find a basis for a solvable Lie algebra which defines an ascending chain of ideals
DifferentialGeometry/LieAlgebras/BracketOfSubspaces
calculate the span of the Lie bracket of two lists of vectors in a Lie algebra, calculate the span of the matrix commutator of two lists of matrices
DifferentialGeometry/LieAlgebras/CartanDecomposition
find a Cartan decomposition of a non-compact semi-simple Lie algebra
DifferentialGeometry/LieAlgebras/CartanInvolution
Calling Sequences
DifferentialGeometry/LieAlgebras/CartanMatricesDetails
Details for Cartan matrices and Dynkin diagrams
DifferentialGeometry/LieAlgebras/CartanMatrix
find the Cartan matrix for a simple Lie algebra from a root space decomposition, display the Cartan matrix for a given root type
DifferentialGeometry/LieAlgebras/CartanMatrixToStandardForm
transform a Cartan matrix to standard form
DifferentialGeometry/LieAlgebras/CartanSubalgebra
find a Cartan subalgebra of a Lie algebra
DifferentialGeometry/LieAlgebras/Center
find the center of a Lie algebra or a non-commutative algebra
DifferentialGeometry/LieAlgebras/Centralizer
find the centralizer of a list of vectors
DifferentialGeometry/LieAlgebras/ChangeGradedComponent
change one or more components of a graded Lie algebra
DifferentialGeometry/LieAlgebras/ChangeLieAlgebraTo
change the current frame to the frame for a Lie algebra
DifferentialGeometry/LieAlgebras/ChangeRepresentationBasis
change the basis for a representation, either in the Lie algebra or in the representation space
DifferentialGeometry/LieAlgebras/ChevalleyBasis
find the Chevalley basis for a real, split semi-simple Lie algebra
DifferentialGeometry/LieAlgebras/CoRoot
find the coroot of a root vector for a semi-simple Lie algebra
DifferentialGeometry/LieAlgebras/Codifferential
calculate the codifferential of a multi-vector defined on a Lie algebra with coefficients in a representation
DifferentialGeometry/LieAlgebras/Cohomology
compute relative Lie algebra cohomology with coefficients in a representation
DifferentialGeometry/LieAlgebras/CompactRoots
find the compact roots in a root system for a non-compact semi-simple real Lie algebra
DifferentialGeometry/LieAlgebras/Complexify
LieAlgebras[Complexify] find the complexification of a Lie algebra
DifferentialGeometry/LieAlgebras/Decompose
decompose a Lie algebra into a direct sum of indecomposable Lie algebras
DifferentialGeometry/LieAlgebras/Deformation
find the deformation of a Lie algebra defined by a list of 2-forms
DifferentialGeometry/LieAlgebras/Derivations
find the derivations of a Lie algebra, find the derivations of a general non-commutative algebra
DifferentialGeometry/LieAlgebras/DerivedAlgebra
find the derived algebra of a Lie algebra
DifferentialGeometry/LieAlgebras/DirectSum
create the direct sum of a list of Lie algebras
DifferentialGeometry/LieAlgebras/DirectSumOfRepresentations
form the direct sum representation for a list of representations of a Lie algebra
Page 1 of 1