Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Derived Picard groups of symmetric representation-finite algebras of
  type $D$   We explicitly describe the derived Picard groups of symmetric
representation-finite algebras of type $D$. In particular, we prove that these
groups are generated by spherical twists along collections of $0$-spherical
objects, the shift and autoequivalences which come from outer automorphisms of
a particular representative of the derived equivalence class. The arguments we
use are based on the fact that symmetric representation-finite algebras are
tilting-connected. To apply this result we in particular develop a
combinatorial-geometric model for silting mutations in type $D$, generalising
the classical concepts of Brauer trees and Kauer moves. Another key ingredient
in the proof is the faithfulness of the braid group action via spherical twists
along $D$-configurations of $0$-spherical objects.

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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: nlin
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The categories of this paper are: cs
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The categories of this paper are: quant-ph
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: ao-sci
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: eess
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The categories of this paper are: mtrl-th