The UCT theorem is shown in the sreenshot. I have a question : What is the definition of $Ext_{\Bbb Z}^1(K_{*}(A),K_{*}(B))$? Does it have a relationship with Tor functor?
2026-03-25 09:24:20.1774430660
Univesal Coefficient Theorem for $C^*$-algebras
63 Views Asked by user63181 https://math.techqa.club/user/user63181/detail AtRelated Questions in OPERATOR-THEORY
- $\| (I-T)^{-1}|_{\ker(I-T)^\perp} \| \geq 1$ for all compact operator $T$ in an infinite dimensional Hilbert space
- Confusion about relationship between operator $K$-theory and topological $K$-theory
- Definition of matrix valued smooth function
- hyponormal operators
- a positive matrix of operators
- If $S=(S_1,S_2)$ hyponormal, why $S_1$ and $S_2$ are hyponormal?
- Closed kernel of a operator.
- Why is $\lambda\mapsto(\lambda\textbf{1}-T)^{-1}$ analytic on $\rho(T)$?
- Show that a sequence of operators converges strongly to $I$ but not by norm.
- Is the dot product a symmetric or anti-symmetric operator?
Related Questions in OPERATOR-ALGEBRAS
- Bijection between $\Delta(A)$ and $\mathrm{Max}(A)$
- hyponormal operators
- Cuntz-Krieger algebra as crossed product
- Identifying $C(X\times X)$ with $C(X)\otimes C(X)$
- If $A\in\mathcal{L}(E)$, why $\lim\limits_{n\to+\infty}\|A^n\|^{1/n}$ always exists?
- Given two projections $p,q$ in a C$^{*}$-algebra $E$, find all irreducible representations of $C^{*}(p,q)$
- projective and Haagerup tensor norms
- AF-algebras and K-theory
- How to show range of a projection is an eigenspace.
- Is $\left\lVert f_U-f_V\right\rVert_{op}\leq \left\lVert U-V\right\rVert_2$ where $f_U = A\mapsto UAU^*$?
Related Questions in C-STAR-ALGEBRAS
- Cuntz-Krieger algebra as crossed product
- Given two projections $p,q$ in a C$^{*}$-algebra $E$, find all irreducible representations of $C^{*}(p,q)$
- AF-algebras and K-theory
- How to show range of a projection is an eigenspace.
- Is a $*$-representation $\pi:A\to B(H)$ non-degenerate iff $\overline{\pi(A) B(H)} = B(H)$?
- Spectral theorem for inductive limits of $C^*$-Algebras
- Examples of unbounded approximate units in $C^*$-algebras
- Is there a way to describe these compactifications algebraically?
- Projections in C*-algebras
- Homogeneous C*-algebras
Related Questions in K-THEORY
- Confusion about relationship between operator $K$-theory and topological $K$-theory
- AF-algebras and K-theory
- An immediate result of fundamental theorem of algebraic $K$-theory.
- Opposite effective classes in a Grothendieck group
- Trivial K-theory implies trivial K-theory of hereditary corners?
- Are there examples of unital and nuclear $C^*$-algebras satisfying the UCT that are not groupoid algebras of an amenable etale groupoid?
- Algebraic $K_2$ as "universal receptacle"?
- How is $K(X\times S^2)$ a $K(X)$ module ?
- Traces on $K(H)$
- Adams operations and an artificial grading on K-theory
Related Questions in TOPOLOGICAL-K-THEORY
- Confusion about relationship between operator $K$-theory and topological $K$-theory
- How does the class of the tangent bundle behave in the K-theory ring?
- What is a "formal" difference of vector bundles?
- Analytic Grothendieck Riemann Roch
- Vector bundle over projective space
- Definition of a (topologically) continuous functor
- How is $K(X\times S^2)$ a $K(X)$ module ?
- Tietze extension theorem for vector bundles on paracompact spaces
- question about the Thom space
- homotopy cofibers (Thom spaces)
Trending Questions
- Induction on the number of equations
- How to convince a math teacher of this simple and obvious fact?
- Find $E[XY|Y+Z=1 ]$
- Refuting the Anti-Cantor Cranks
- What are imaginary numbers?
- Determine the adjoint of $\tilde Q(x)$ for $\tilde Q(x)u:=(Qu)(x)$ where $Q:U→L^2(Ω,ℝ^d$ is a Hilbert-Schmidt operator and $U$ is a Hilbert space
- Why does this innovative method of subtraction from a third grader always work?
- How do we know that the number $1$ is not equal to the number $-1$?
- What are the Implications of having VΩ as a model for a theory?
- Defining a Galois Field based on primitive element versus polynomial?
- Can't find the relationship between two columns of numbers. Please Help
- Is computer science a branch of mathematics?
- Is there a bijection of $\mathbb{R}^n$ with itself such that the forward map is connected but the inverse is not?
- Identification of a quadrilateral as a trapezoid, rectangle, or square
- Generator of inertia group in function field extension
Popular # Hahtags
second-order-logic
numerical-methods
puzzle
logic
probability
number-theory
winding-number
real-analysis
integration
calculus
complex-analysis
sequences-and-series
proof-writing
set-theory
functions
homotopy-theory
elementary-number-theory
ordinary-differential-equations
circles
derivatives
game-theory
definite-integrals
elementary-set-theory
limits
multivariable-calculus
geometry
algebraic-number-theory
proof-verification
partial-derivative
algebra-precalculus
Popular Questions
- What is the integral of 1/x?
- How many squares actually ARE in this picture? Is this a trick question with no right answer?
- Is a matrix multiplied with its transpose something special?
- What is the difference between independent and mutually exclusive events?
- Visually stunning math concepts which are easy to explain
- taylor series of $\ln(1+x)$?
- How to tell if a set of vectors spans a space?
- Calculus question taking derivative to find horizontal tangent line
- How to determine if a function is one-to-one?
- Determine if vectors are linearly independent
- What does it mean to have a determinant equal to zero?
- Is this Batman equation for real?
- How to find perpendicular vector to another vector?
- How to find mean and median from histogram
- How many sides does a circle have?