Not signed in

Want to take part in these discussions? Sign in if you have an account, or apply for one below

• Username
• Password
• Remember me

• Sign in using OpenID
• Remember me

• Forgot your password?
• Apply for membership

2-category 2-category-theory abelian-categories adjoint algebra algebraic algebraic-geometry algebraic-topology analysis analytic-geometry arithmetic arithmetic-geometry book bundles calculus categorical categories category category-theory chern-weil-theory cohesion cohesive-homotopy-type-theory cohomology colimits combinatorics complex complex-geometry computable-mathematics computer-science constructive cosmology definitions deformation-theory descent diagrams differential differential-cohomology differential-equations differential-geometry digraphs duality elliptic-cohomology enriched fibration foundation foundations functional-analysis functor gauge-theory gebra geometric-quantization geometry graph graphs gravity grothendieck group group-theory harmonic-analysis higher higher-algebra higher-category-theory higher-differential-geometry higher-geometry higher-lie-theory higher-topos-theory homological homological-algebra homotopy homotopy-theory homotopy-type-theory index-theory integration integration-theory k-theory lie-theory limits linear linear-algebra locale localization logic mathematics measure-theory modal modal-logic model model-category-theory monad monads monoidal monoidal-category-theory morphism motives motivic-cohomology nforum nlab noncommutative noncommutative-geometry number-theory of operads operator operator-algebra order-theory pages pasting philosophy physics pro-object probability probability-theory quantization quantum quantum-field quantum-field-theory quantum-mechanics quantum-physics quantum-theory question representation representation-theory riemannian-geometry scheme schemes set set-theory sheaf simplicial space spin-geometry stable-homotopy-theory stack string string-theory superalgebra supergeometry svg symplectic-geometry synthetic-differential-geometry terminology theory topology topos topos-theory tqft type type-theory universal variational-calculus

1. • CommentRowNumber1.
   • CommentAuthorTobyBartels
   • CommentTimeOct 2nd 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexI wrote about the boolean algebra of [[idempotents]] in a commutative ring. There's also stuff in there about [[projection operator]]s (that page doesn't exist).

   I wrote about the boolean algebra of idempotents in a commutative ring. There’s also stuff in there about projection operators (that page doesn’t exist).

2. • CommentRowNumber2.
   • CommentAuthorEric
   • CommentTimeOct 3rd 2011
   • PermaLink
   Author: Eric
   Format: MarkdownItexIs there anything special about the case where the sum of all idempotents is equal to the identity? It's probably not too interesting to anyone, but at some point I wrote: [algebra of projections](http://ncatlab.org/ericforgy/show/algebra+of+projections). I was interested in this because whenever you have a complete set of projections, you can define a graded differential (noncommutative) calculus on them. That calculus and/or it's cohomology might be interesting.

   Is there anything special about the case where the sum of all idempotents is equal to the identity?

   It’s probably not too interesting to anyone, but at some point I wrote: algebra of projections.

   I was interested in this because whenever you have a complete set of projections, you can define a graded differential (noncommutative) calculus on them. That calculus and/or it’s cohomology might be interesting.

3. • CommentRowNumber3.
   • CommentAuthorTobyBartels
   • CommentTimeOct 3rd 2011
   • PermaLink
   Author: TobyBartels
   Format: MarkdownItexThey're not the same thing, but related. I'm taking the algebra consisting of all projections in a commutative algebra, which is typically an uncountable set with an infinite sum. You're taking a set of only countably many of the projections in a typically noncommutative algebra and requiring the sum to be finite.

   They’re not the same thing, but related. I’m taking the algebra consisting of all projections in a commutative algebra, which is typically an uncountable set with an infinite sum. You’re taking a set of only countably many of the projections in a typically noncommutative algebra and requiring the sum to be finite.