String Applet

An interactive tool for computations with special biserial algebras, string algebras, and gentle algebras.
It displays many combinatorial invariants of these algebras and their module categories.

Load
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Save
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Export
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Special Biserial Algebra

General Information
Strings
τ-Tilting
References

Dimensions

Indecomposables

Cartan Matrix

Complete Derived Invariant

Nakayama Permutation

String Components of the AR Quiver

Click on a string to get more information.

Biserial Projective-Injectives

Elementary Strings

Elementary Cyclic Strings

Elementary Bands

Forbidden Cycles

Alternating Cycles

Surface Quiver

String Quiver

Reduced Syzygy Quiver

Bridge Quiver

To mutate, click on a summand.

τ-Rigid Part

Support Part

G-Matrix

Feedback is welcome. Please let me know if you encounter bugs or miscalculations.

Articles

Name

Positive AR Translate

Negative AR Translate

Direct AR Predecessors

Direct AR Successors

Positive Syzygy

Negative Syzygy

The quiver may have many vertices.

Compute it anyway?